\begin{thebibliography}{100} \expandafter\ifx\csname url\endcsname\relax \def\url#1{\texttt{#1}}\fi \expandafter\ifx\csname urlprefix\endcsname\relax\def\urlprefix{URL }\fi \bibitem{Lestel05} D.~Lestel, C.~Herzfeld, Topological apes: Knots tying and untying and the origins of mathematics, in: P.~Grialou, G.~Longo, M.~Okada (Eds.), Image and Reasoning, Vol.~1, Tokyo: University of Keio Press, 2005, pp. 147--162. \bibitem{Herzfeld05} C.~Herzfeld, D.~Lestel, Knot tying in great apes: etho-ethnology of an unusual tool behavior, Social Science Information 44 (2005) 621--653. \bibitem{Newton1687} I.~Newton, {P}hilosophi{\ae} {N}aturalis {P}rincipia {M}athematica, London, 1687. \bibitem{Ehrenfest1917} P.~Ehrenfest, Proc. Amsterdam Acad. 20 (1917) 200. \bibitem{Ehrenfest1920} P.~Ehrenfest, {W}elche {R}olle spielt die {D}reidimensionalit\"{a}t des {R}aumes in den {G}rundgesetzen der {P}hysik?, Ann. Physik 61 (1920) 440. \bibitem{Tangherlini63} F.~R. Tangherlini, Schwarzschild field in {$n$} dimensions and the dimensionality of space problem, Nuovo Cimento (10) 27 (1963) 636--651. \bibitem{Buchel63} W.~B\"{u}chel, {W}arum hat der {R}aum drei {D}imensionen?, Physikalische Bl\"{a}tter 19 (1963) 547--549, {E}nglish translation in~\cite{Freeman69}. \bibitem{Bose1924} S.~N. Bose, {P}lancks {G}esetz und {L}ichtquantenhypothese, Zeits. f. Physik 26 (1924) 178--181. \bibitem{Einstein1924} A.~Einstein, {Q}uantentheorie des einatomigen idealen {G}ases, in: Sitzungsber. Kgl. Preuss. Akad. Wiss., 1924, pp. 261--267. \bibitem{Fermi1926} E.~Fermi, Zur {Q}uantelung des idealen einatomigen {G}ases, Zeits. f. Physik 36 (1926) 902. \bibitem{Dirac1926} P.~A.~M. Dirac, On the theory of quantum mechanics, Proc. Roy. Soc. A112 (1926) 661--677. \bibitem{Born1926} M.~Born, Zur {Q}uantenmechanik der {S}to{\ss}vorg\"{a}nge, Zeits. f. Physik 37 (1926) 863--867. \bibitem{Fadell62} E.~Fadell, L.~Neuwirth, Configuration spaces, Math. Scand. 10 (1962) 111--118. \bibitem{Feynman48} R.~P. Feynman, Space-time approach to non-relativistic quantum mechanics, Rev. Mod. Phys. 20 (1948) 367--387. \bibitem{Laidlaw71} M.~G.~G. Laidlaw, C.~M. DeWitt, Feynman functional integrals for systems of indistinguishable particles, Phys. Rev. D 3 (1971) 1375--1378. \bibitem{Green53} H.~S. Green, A generalized method of field quantization, Phys. Rev. 90 (1953) 270--273. \bibitem{Druhl70} K.~Dr\"{u}hl, R.~Haag, J.~E. Roberts, On parastatistics, Commun. Math. Phys. 18 (1970) 204--226. \bibitem{Leinaas77} J.~M. Leinaas, J.~Myrheim, On the theory of identical particles, Nuovo Cimento B 37B (1977) 1. \bibitem{Artin1926} E.~Artin, {T}heorie der {Z}\"{o}pfe, Abh. math. Sem. Hamburg 4 (1926) 47--72. \bibitem{Wilczek82a} F.~Wilczek, Magnetic flux, angular momentum, and statistics, Phys. Rev. Lett. 48 (1982) 1144--1146. \bibitem{Wilczek82b} F.~Wilczek, Quantum mechanics of fractional-spin particles, Phys. Rev. Lett. 49 (1982) 957--959. \bibitem{Goldin85} G.~A. Goldin, R.~Menikoff, D.~H. Sharp, Comments on ``{G}eneral {T}heory for {Q}uantum {S}tatistics in {T}wo {D}imensions'', Phys. Rev. Lett. 54 (1985) 603. \bibitem{Imbo90} T.~D. Imbo, J.~March-Russell, Exotic statistics on surfaces, Phys. Lett. B 252 (1990) 84--90. \bibitem{Moore88} G.~Moore, N.~Seiberg, Polynomial equations for rational conformal field theories, Phys. Lett. B 212 (1988) 451--460. \bibitem{Moore89b} G.~Moore, N.~Seiberg, Classical and quantum conformal field theory, Commun. Math. Phys. 123 (1989) 177--254. \bibitem{Witten89} E.~Witten, Quantum field theory and the {J}ones polynomial, Comm. Math. Phys. 121 (1989) 351--399. \bibitem{Fredenhagen89} K.~Fredenhagen, K.~H. Rehren, B.~Schroer, Superselection sectors with braid group statistics and exchange algebras, Commun. Math. Phys. 125 (1989) 201--226. \bibitem{Froehlich90} J.~Fr\"{o}hlich, F.~Gabbiani, Braid statistics in local quantum theory, Rev. Math. Phys. 2 (1990) 251--353. \bibitem{Turaev94} V.~G. Turaev, Quantum Invariants of Knots and 3-Manifolds, Walter de Gruyter, Berlin, New York, 1994. \bibitem{Kassel95} C.~Kassel, Quantum Groups, Springer-Verlag, New York, Berlin, Heidelberg, 1995. \bibitem{Bakalov01} B.~Bakalov, A.~Kirillov, Lectures on Tensor Categories and Modular Functors, Vol.~21 of University Lecture Series, American Mathematical Society, 2001. \bibitem{Prange87} R.~Prange, S.~M. Girvin (Eds.), The Quantum {H}all effect, Springer-Verlag, New York, 1987. \bibitem{Karlhede92} A.~Karlhede, S.~A. Kivelson, S.~L. Sondhi, The quantum {H}all effect: The article, in: V.~J. Emery (Ed.), Correlated Electron Systems, World Scientific, Singapore, 1992, lectures presented at the 9th Jerusalem Winter School for Theoretical Physics. \bibitem{DasSarma97} S.~Das~Sarma, A.~Pinczek, Perspectives in quantum {H}all effects: Novel quantum liquids in low-dimensional semiconductor structures, Wiley, New York, 1997. \bibitem{Ezawa00} Z.~Ezawa (Ed.), Quantum {H}all effects, field theoretical approach and related topics, World Scientific, Singapore, 2000. \bibitem{Eisenstein90} J.~P. Eisenstein, H.~L. Stormer, The fractional quantum {H}all effect, Science 248 (1990) 1510--1516. \bibitem{Stormer99} H.~L. Stormer, D.~C. Tsui, A.~C. Gossard, The fractional quantum {H}all effect, Rev. Mod. Phys. 71 (1999) S298--S305. \bibitem{von_Klitzing80} K.~von Klitzing, G.~Dorda, M.~Pepper, New method for high-accuracy determination of the fine-structure constant based on quantized {H}all resistance, Phys. Rev. Lett. 45 (1980) 494--497. \bibitem{Tsui82} D.~C. Tsui, H.~L. Stormer, A.~C. Gossard, Two-dimensional magnetotransport in the extreme quantum limit, Phys. Rev. Lett. 48 (1982) 1559--62. \bibitem{Goldman95} V.~J. Goldman, B.~Su, Resonant tunneling in the quantum {H}all regime: Measurement of fractional charge, Science 267 (1995) 1010--1012. \bibitem{Goldman05a} V.~J. Goldman, J.~Liu, A.~Zaslavsky, Fractional statistics of {L}aughlin quasiparticles in quantum antidots, Phys. Rev. B 71 (2005) 153303. \bibitem{Camino05a} F.~E. Camino, W.~Zhou, V.~J. Goldman, Realization of a {L}aughlin quasiparticle interferometer: Observation of fractional statistics, Phys. Rev. B 72 (2005) 075342, cond-mat/0502406. \bibitem{Camino05b} F.~E. Camino, W.~Zhou, V.~J. Goldman, {A}haronov--{B}ohm superperiod in a {L}aughlin quasiparticle interferometer, Phys. Rev. Lett. 95 (2005) 246802, cond-mat/0504341. \bibitem{Camino06a} F.~E. Camino, W.~Zhou, V.~J. Goldman, Transport in the {L}aughlin quasiparticle interferometer: Evidence for topological protection in an anyonic qubit, Phys. Rev. B 74 (2006) 115301, cond-mat/0606742. \bibitem{Camino07a} F.~E. Camino, W.~Zhou, V.~J. Goldman, $e/3$ {L}aughlin quasiparticle primary-filling $\nu=1/3$ interferometer, Phys. Rev. Lett. 98 (2007) 076805, cond-mat/0610751. \bibitem{Camino07b} F.~E. Camino, W.~Zhou, V.~J. Goldman, Experimental realization of a primary-filling e/3 quasiparticle interferometer (2006), cond-mat/0611443. \bibitem{Moore91} G.~Moore, N.~Read, Nonabelions in the fractional quantum {H}all effect, Nucl. Phys. B 360 (1991) 362--396. \bibitem{Laughlin83} R.~B. Laughlin, Anomalous quantum {H}all effect: an incompressible quantum fluid with fractionally charged excitations, Phys. Rev. Lett. 50 (1983) 1395--8. \bibitem{Willett87} R.~Willett, J.~P. Eisenstein, H.~L. Stormer, D.~C. Tsui, A.~C. Gossard, J.~H. English, Observation of an even-denominator quantum number in the fractional quantum {H}all effect, Phys. Rev. Lett. 59 (1987) 1776--9. \bibitem{Pan99} W.~Pan, J.-S. Xia, V.~Shvarts, D.~E. Adams, H.~L. Stormer, D.~C. Tsui, L.~N. Pfeiffer, K.~W. Baldwin, K.~W. West, Exact quantization of the even-denominator fractional quantum {H}all state at $\nu=5/2$ {L}andau level filling factor, Phys. Rev. Lett. 83 (1999) 3530--3, cond-mat/9907356. \bibitem{Eisenstein02} J.~P. Eisenstein, K.~B. Cooper, L.~N. Pfeiffer, K.~W. West, Insulating and fractional quantum {H}all states in the first excited {L}andau level, Phys. Rev. Lett. 88 (2002) 076801, cond-mat/0110477. \bibitem{Xia04} J.~S. Xia, W.~Pan, C.~L. Vicente, E.~D. Adams, N.~S. Sullivan, H.~L. Stormer, D.~C. Tsui, L.~N. Pfeiffer, K.~W. Baldwin, K.~W. West, Electron correlation in the second {L}andau level: A competition between many nearly degenerate quantum phases, Phys. Rev. Lett. 93 (2004) 176809, cond-mat/0406724. \bibitem{Read99} N.~Read, E.~Rezayi, Beyond paired quantum {H}all states: Parafermions and incompressible states in the first excited {L}andau level, Phys. Rev. B 59 (1999) 8084--–8092, cond-mat/9809384. \bibitem{Morf98} R.~H. Morf, Transition from quantum {H}all to compressible states in the second {L}andau level: new light on the $\nu=5/2$ enigma, Phys. Rev. Lett. 80 (1998) 1505--8, cond-mat/9809024. \bibitem{Rezayi00} E.~H. Rezayi, F.~D.~M. Haldane, Incompressible paired {H}all state, stripe order, and the composite fermion liquid phase in half-filled {L}andau levels, Phys. Rev. Lett. 84 (2000) 4685--4688, cond-mat/9906137. \bibitem{Nayak96c} C.~Nayak, F.~Wilczek, $2n$-quasihole states realize $2^{n-1}$-dimensional spinor braiding statistics in paired quantum {H}all states, Nucl. Phys. B 479 (1996) 529--53, cond-mat/9605145. \bibitem{Slingerland01} J.~K. Slingerland, F.~A. Bais, Quantum groups and nonabelian braiding in quantum {H}all systems, Nucl. Phys. B 612 (2001) 229--290, cond-mat/0104035. \bibitem{Read00} N.~Read, D.~Green, Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries and the fractional quantum {H}all effect, Phys. Rev. B 61 (2000) 10267--10297, cond-mat/9906453. \bibitem{Ivanov01} D.~A. Ivanov, Non-{A}belian statistics of half-quantum vortices in p-wave superconductors, Phys. Rev. Lett. 86 (2001) 268--271, cond-mat/0005069. \bibitem{Stern04} A.~Stern, F.~von Oppen, E.~Mariani, Geometric phases and quantum entanglement as building blocks for non-{A}belian quasiparticle statistics, Phys. Rev. B 70 (2004) 205338, cond-mat/0310273. \bibitem{Ardonne99} E.~Ardonne, K.~Schoutens, A new class of non-{A}belian spin-singlet quantum {H}all states, Phys. Rev. Lett. 82~(25) (1999) 5096--5099, cond-mat/9811352. \bibitem{Kitaev97} A.~Y. Kitaev, Fault-tolerant quantum computation by anyons, Ann. Phys. 303 (2003) 2, quant-ph/9707021. \bibitem{Kitaev06a} A.~Kitaev, Anyons in an exactly solved model and beyond, Ann. Phys. 321 (2006) 2--111, cond-mat/0506438. \bibitem{Freedman03} M.~H. Freedman, A magnetic model with a possible {C}hern-{S}imons phase, Commun. Math. Phys. 234 (2003) 129--183, quant-ph/0110060. \bibitem{Freedman04a} M.~Freedman, C.~Nayak, K.~Shtengel, K.~Walker, Z.~Wang, A class of ${P,T}$-invariant topological phases of interacting electrons, Ann. Phys. 310 (2004) 428--492, cond-mat/0307511. \bibitem{Freedman05a} M.~Freedman, C.~Nayak, K.~Shtengel, Extended {H}ubbard model with ring exchange: A route to a non-{A}belian topological phase, Phys. Rev. Lett. 94 (2005) 066401, cond-mat/0312273. \bibitem{Freedman05b} M.~Freedman, C.~Nayak, K.~Shtengel, Line of critical points in $2+1$ dimensions: Quantum critical loop gases and non-{A}belian gauge theory, Phys. Rev. Lett. 94 (2005) 147205, cond-mat/0408257. \bibitem{Turaev92} V.~G. Turaev, O.~Y. Viro, State sum invariants of 3-manifolds and quantum 6j-symbols, Topology 31 (1992) 865--902. \bibitem{Levin05a} M.~A. Levin, X.-G. Wen, String-net condensation: A physical mechanism for topological phases, Phys. Rev. B 71 (2005) 045110, cond-mat/0404617. \bibitem{Fendley05a} P.~Fendley, E.~Fradkin, Realizing non-{A}belian statistics in time-reversal-invariant systems, Phys. Rev. B 72 (2005) 024412, cond-mat/0502071. \bibitem{Fidkowski07a} L.~Fidkowski, From string nets to nonabelions (2006), cond-mat/0610583. \bibitem{Doucot04} B.~Dou\c{c}ot, L.~B. Ioffe, J.~Vidal, Discrete non-{A}belian gauge theories in {J}osephson-junction arrays and quantum computation, Phys. Rev. B 69 (2004) 214501, cond-mat/0302104. \bibitem{DasSarma06a} S.~D. Sarma, C.~Nayak, S.~Tewari, Proposal to stabilize and detect half-quantum vortices in strontium ruthenate thin films: Non-{A}belian braiding statistics of vortices in a $p_ x + ip_y$ superconductor, Phys. Rev. B 73 (2006) 220502, cond-mat/0510553. \bibitem{Tewari07a} S.~Tewari, S.~D. Sarma, C.~Nayak, C.~Zhang, P.~Zoller, Quantum computation using vortices and majorana zero modes of a $p_x + ip_y$ superfluid of fermionic cold atoms, Phys. Rev. Lett. 98 (2007) 010506, quant-ph/0606101. \bibitem{Gurarie05a} V.~Gurarie, L.~Radzihovsky, A.~V. Andreev, Quantum phase transitions across a $p$-wave {F}eshbach resonance, Phys. Rev. Lett. 94 (2005) 230403, cond-mat/0410620. \bibitem{Cooper01a} N.~R. Cooper, N.~K. Wilkin, J.~M.~F. Gunn, Quantum phases of vortices in rotating {B}ose--{E}instein condensates, Phys. Rev. Lett. 87 (2001) 120405, cond-mat/0107005. \bibitem{Cooper04a} N.~R. Cooper, Exact ground states of rotating {B}ose gases close to a {F}eshbach resonance, Physical Review Letters 92 (2004) 220405, cond-mat/0107005. \bibitem{Rezayi05} E.~H. Rezayi, N.~Read, N.~R. Cooper, Incompressible liquid state of rapidly rotating bosons at filling factor 3/2, Phys. Rev. Lett. 95 (2005) 160404, cond-mat/0507064. \bibitem{Preskill98} J.~Preskill, Fault-tolerant quantum computation, in: H.-K. Lo, S.~Popescu, T.~P. Spiller (Eds.), Introduction to Quantum Computation, World Scientific, 1998. \bibitem{Ogburn99} R.~W. Ogburn, J.~Preskill, Topological quantum computation, Lect. Notes in Comp. Sci. 1509 (1999) 341--356. \bibitem{Freedman01} M.~H. Freedman, Quantum computation and the localization of modular functors, Found. Comput. Math. 1 (2001) 183--204, quant-ph/0003128. \bibitem{Freedman02a} M.~H. Freedman, M.~J. Larsen, Z.~Wang, A modular functor which is universal for quantum computation, Commun. Math. Phys. 227 (2002) 605--622, quant-ph/0001108. \bibitem{FKLW} M.~Freedman, A.~Kitaev, M.~Larsen, Z.~Wang, Topological quantum computation, quant-ph/0101025 (2001). \bibitem{Mochon03} C.~Mochon, Anyons from nonsolvable finite groups are sufficient for universal quantum computation, Phys. Rev. A 67 (2003) 022315, quant-ph/0206128. \bibitem{Mochon04} C.~Mochon, Anyon computers with smaller groups, Phys. Rev. A 69 (2004) 032306, quant-ph/0306063. \bibitem{DasSarma05} S.~Das~Sarma, M.~Freedman, C.~Nayak, Topologically protected qubits from a possible non-{A}belian fractional quantum {H}all state, Phys. Rev. Lett. 94 (2005) 166802, cond-mat/0412343. \bibitem{FNW05a} M.~Freedman, C.~Nayak, K.~Walker, Towards universal topological quantum computation in the $\nu=5/2$ fractional quantum {H}all state (2005), cond-mat/0512066. \bibitem{FNW05b} M.~Freedman, C.~Nayak, K.~Walker, Tilted interferometry realizes universal quantum computation in the {I}sing {TQFT} without overpasses (2005), cond-mat/0512072. \bibitem{Bravyi06} S.~Bravyi, Universal quantum computation with the $\nu=5/2$ fractional quantum {H}all state, Phys. Rev. A 73 (2006) 042313, quant-ph/0511178. \bibitem{Bonesteel05} N.~E. Bonesteel, L.~Hormozi, G.~Zikos, S.~H. Simon, Braid topologies for quantum computation, Phys. Rev. Lett. 95 (2005) 140503, quant-ph/0505065. \bibitem{Simon06a} S.~H. Simon, N.~E. Bonesteel, M.~H. Freedman, N.~Petrovic, L.~Hormozi, Topological quantum computing with only one mobile quasiparticle, Phys. Rev. Lett. 96 (2006) 070503, quant-ph/0509175. \bibitem{Hormozi07a} L.~Hormozi, G.~Zikos, N.~E. Bonesteel, S.~H. Simon, Topological quantum compiling, Phys. Rev. B 75 (2007) 165310, quant-ph/0610111. \bibitem{Aharonov59} Y.~Aharonov, D.~Bohm, Significance of electromagnetic potentials in the quantum theory, Phys. Rev. 115 (1959) 485--491. \bibitem{Braginsky75} V.~B. Braginsky, Y.~I. Vorontsov, Usp. Fiz. Nauk 41--62 (1974) 114, [Sov. Phys. Uspekhi 17, 644 (1975)]. \bibitem{Preskill-lectures} J.~Preskill, Topological quantum computation, lecture notes (2004). \newline\urlprefix\url{http://www.theory.caltech.edu/~preskill/ph219/topologic% al.ps} \bibitem{MacLane98} S.~Mac~Lane, {C}ategories for the {W}orking {M}athematician, 2nd Edition, {G}raduate {T}exts in {M}athematics, Springer-Verlag, New York, 1998. \bibitem{Buchberger65} B.~Buchberger, Ein {A}lgorithmus zum {A}uffinden der {B}asiselemente des {R}estklassenringes nach einem nulldimensionalen {P}olynomideal, Ph.D. thesis, {E}nglish translation in~\cite{Buchberger06} (1965). \bibitem{Buchberger70} B.~Buchberger, Ein algorithmisches {K}riterium f\"{u}r die {L}\"{o}sbarkeit eines algebraischen {G}leichungssystems, Aequationes mathematicae 4 (1970) 374--383, {E}nglish translation in~\cite{Buchberger98}. \bibitem{Etingof05} P.~Etingof, D.~Mikshych, V.~Ostrik, On fusion categories, Ann. Math. 162 (2005) 581--642. \bibitem{Zehnder1891} L.~Zehnder, Ein neuer interferenzrefractor, Zeitschr. f. Instrkde. 11 (1891) 275--285. \bibitem{Mach1892} L.~Mach, \"{U}ber einer interferenzrefractor, Zeitschr. f. Instrkde. 12 (1892) 89--93. \bibitem{Bonderson07a} P.~Bonderson, K.~Shtengel, J.~K. Slingerland, Decoherence of anyonic charge in interferometry measurements, Phys. Rev. Lett. 98 (2007) 070401, quant-ph/0608119. \bibitem{Overbosch01} B.~J. Overbosch, F.~A. Bais, Inequivalent classes of interference experiments with non-{A}belian anyons, Phys. Rev. A 64 (2001) 062107, quant-ph/0105015. \bibitem{Zeilinger81} A.~Zeilinger, General properties of lossless beam splitters in interferometry, Am. J. Phys. 49 (1981) 882--883. \bibitem{Bonderson06b} P.~Bonderson, K.~Shtengel, J.~K. Slingerland, Probing non-{A}belian statistics with quasiparticle interferometry, Phys. Rev. Lett. 97 (2006) 016401, cond-mat/0601242. \bibitem{Ji03} Y.~Ji, Y.~Chung, D.~Sprinzak, M.~Heiblum, D.~Mahalu, H.~Shtrikman, An electronic {M}ach--{Z}ehnder interferometer, Nature 422 (2003) 415--418, cond-mat/0303553. \bibitem{Neder05} I.~Neder, M.~Heiblum, Y.~Levinson, D.~Mahalu, V.~Umansky, Coherence and phase in an electronic {M}ach--{Z}ehnder interferometer: An unexpected behavior of interfering electrons (2005), cond-mat/0508024. \bibitem{Neder06} I.~Neder, M.~Heiblum, Y.~Levinson, D.~Mahalu, V.~Umansky, Unexpected behavior in a two-path electron interferometer, Phys. Rev. Lett. 96 (2006) 016804. \bibitem{Kane03} C.~L. Kane, Telegraph noise and fractional statistics in the quantum {H}all effect, Phys. Rev. Lett. 90 (2003) 226802, cond-mat/0210621. \bibitem{Jonckheere05} T.~Jonckheere, P.~Devillard, A.~Crepieux, T.~Martin, Electronic {Mach}--{Z}ehnder interferometer in the fractional quantum {H}all effect, Phys. Rev. B 72 (2005) 201305(R), cond-mat/0503617. \bibitem{Law06} K.~T. Law, D.~E. Feldman, Y.~Gefen, Electronic {M}ach-{Z}ehnder interferometer as a tool to probe fractional statistics, Phys. Rev. B 74 (2006) 045319, cond-mat/0506302. \bibitem{Feldman06} D.~E. Feldman, A.~Kitaev, Detecting non-{A}belian statistics with an electronic {M}ach--{Z}ehnder interferometer, Phys. Rev. Lett. 97 (2006) 186803, cond-mat/0607541. \bibitem{Fabry1897} C.~Fabry, A.~P\'{e}rot, Sur les franges des lames minces argente\'{e}s et leur application \`{a} la mesure de petites \'{e}paisseurs d{'}air, Ann. Chim. Phys. 12 (1897) 459--501. \bibitem{Chamon97} C.~de~C.~Chamon, D.~E. Freed, S.~A. Kivelson, S.~L. Sondhi, X.~G. Wen, Two point-contact interferometer for quantum {H}all systems, Phys. Rev. B 55 (1997) 2331--43, cond-mat/9607195. \bibitem{Fradkin98} E.~Fradkin, C.~Nayak, A.~Tsvelik, F.~Wilczek, A {C}hern-{S}imons effective field theory for the {P}faffian quantum {H}all state, Nucl. Phys. B 516 (1998) 704--18, cond-mat/9711087. \bibitem{Stern06a} A.~Stern, B.~I. Halperin, Proposed experiments to probe the non-abelian $\nu=5/2$ quantum {H}all state, Phys. Rev. Lett. 96 (2006) 016802, cond-mat/0508447. \bibitem{Bonderson06a} P.~Bonderson, A.~Kitaev, K.~Shtengel, Detecting non-{A}belian statistics in the $\nu=5/2$ fractional quantum {H}all state, Phys. Rev. Lett. 96 (2006) 016803, cond-mat/0508616. \bibitem{Grosfeld06b} E.~Grosfeld, S.~H. Simon, A.~Stern, Switching noise as a probe of statistics in the fractional quantum {H}all effect, Phys. Rev. Lett. 96 (2006) 226803, cond-mat/0602634. \bibitem{Hou06} C.-Y. Hou, C.~Chamon, ``{W}ormhole'' geometry for entrapping topologically protected qubits in non-{A}belian quantum {H}all states and probing them with voltage and noise measurements, Phys. Rev. Lett. 97 (2006) 146802, cond-mat/0603142. \bibitem{Fendley06a} P.~Fendley, M.~P. Fisher, C.~Nayak, Dynamical disentanglement across a point contact in a non-{A}belian quantum {H}all state, Phys. Rev. Lett. 97 (2006) 036801, cond-mat/0604064. \bibitem{Fendley07a} P.~Fendley, M.~P. Fisher, C.~Nayak, Edge states and tunneling of non-{A}belian quasiparticles in the $\nu=5/2$ quantum {H}all state and p+ip superconductors, Phys. Rev. B 75 (2007) 045317, cond-mat/0607431. \bibitem{Chung06} S.~B. Chung, M.~Stone, Proposal for reading out anyon qubits in non-{A}belian $\nu = 12/5$ quantum {H}all state, Phys. Rev. B 73 (2006) 245311, cond-mat/0601594. \bibitem{Fidkowski07c} L.~Fidkowski, Double point contact in the k=3 {R}ead--{R}ezayi state (2007), arXiv:0704.3291. \bibitem{Kim06e} E.-A. Kim, Aharanov-bohm interference and fractional statistics in a quantum hall interferometer, Phys. Rev. Lett. 97 (2006) 216404, cond-mat/0604359. \bibitem{Rosenow07a} B.~Rosenow, B.~I. Halperin, Influence of interactions on flux and back-gate period of quantum {H}all interferometers, Phys. Rev. Lett. 98 (2007) 106801, cond-mat/0611101. \bibitem{Gefen91} D.~J. Thouless, Y.~Gefen, Fractional quantum {H}all effect and multiple {A}haronov--{B}ohm periods, Phys. Rev. Lett. 66 (1991) 806--809. \bibitem{Wen92b} X.~G. Wen, Theory of the edge states in fractional quantum {H}all effects, Intl. J. Mod. Phys. B 6 (1992) 1711--62. \bibitem{Miller07a} J.~B. Miller, I.~P. Radu, D.~M. Zumbuhl, E.~M. Levenson-Falk, M.~A. Kastner, C.~M. Marcus, L.~N. Pfeiffer, K.~W. West, Fractional quantum {H}all effect in a quantum point contact at filling fraction 5/2 (2007), cond-mat/0703161. \bibitem{Dijkgraaf89} R.~Dijkgraaf, C.~Vafa, E.~Verlinde, H.~Verlinde, The operator algebra of orbifold models, Commun. Math. Phys. 123 (1989) 485--526. \bibitem{Dijkgraaf90a} R.~Dijkgraaf, V.~Pasquier, P.~Roche, Quasi {H}opf algebras, group cohomology and orbifold models, Nucl. Phys. B (Proc. Suppl.) 18B (1990) 60--72. \bibitem{Bais92} F.~A. Bais, P.~van Driel, M.~de~Wild~Propitius, Quantum symmetries in discrete gauge theories, Phys. Lett. B 280 (1992) 63--70, hep-th/9203046. \bibitem{Wess71} J.~Wess, B.~Zumino, Consequences of anomalous {W}ard identities, Phys. Lett. B 37 (1971) 95. \bibitem{Witten83} E.~Witten, Global aspects of current algebra, Nucl. Phys. B 223 (1983) 422--432. \bibitem{Jones85} V.~F.~R. Jones, A polynomial invariant for knots via von {N}eumann algebras, Bull. Am. Math. Soc. 12 (1985) 103--111. \bibitem{KuperbergU} G.~Kuperberg, unpublished. \bibitem{Freedman02b} M.~H. Freedman, M.~J. Larsen, Z.~Wang, The two-eigenvalue problem and density of jones representation of braid groups, Commun. Math. Phys. 228 (2002) 177--199. \bibitem{Moore89c} G.~Moore, N.~Seiberg, Taming the conformal zoo, Phys. Lett. B 220 (1989) 422--430. \bibitem{Gepner89} D.~Gepner, Field identification in coset conformal field theories, Phys. Lett. B 222~(2) (1989) 207--212. \bibitem{Zamolodchikov85} A.~B. Zamolodchikov, V.~Fateev, Nonlocal (parafermion) currents in two-dimensional conformal quantum field theory and self-dual critical points in $z_{N}$-symmetric statistical systems, Soviet Physics - JETP 62 (1985) 215--225. \bibitem{Gepner87} D.~Gepner, Z.~Qiu, Modular invariant partition functions for parafermionic field theories, Nucl. Phys. B 285 (1987) 423--453. \bibitem{BondersonWIP} P.~Bonderson, J.~K. Slingerland, in preparation. \bibitem{Schwarz78} A.~S. Schwarz, The partition function of degenerate quadratic functional and {R}ay-{S}inger invariants, Lett. Math. Phys. 2 (1978) 247--252. \bibitem{Schonfeld80} J.~F. Schonfeld, A mass term for three-dimensional gauge fields, Nucl. Phys. B 185 (1981) 157. \bibitem{Deser81} S.~Deser, R.~Jackiw, S.~Templeton, Topologically massive gauge theories, Ann. Phys. 140 (1982) 372--411. \bibitem{Dijkgraaf90} R.~Dijkgraaf, E.~Witten, Topological gauge theories and group cohomology, Commun. Math. Phys. 129 (1990) 393--429. \bibitem{Wen92a} X.~G. Wen, A.~Zee, Classification of {A}belian quantum {H}all states and matrix formulation of topological fluids, Phys. Rev. B 46 (1992) 2290--301. \bibitem{Haldane83} F.~D.~M. Haldane, Fractional quantization of the {H}all effect: A hierarchy of incompressible quantum fluid states, Phys. Rev. Lett. 51 (1983) 605--608. \bibitem{Halperin84} B.~I. Halperin, Statistics of quasiparticles and the hierarchy of fractional quantized {H}all states, Phys. Rev. Lett. 52 (1984) 1583--6. \bibitem{Jain89} J.~K. Jain, Composite fermion approach for the fractional quantum {H}all effect, Phys. Rev. Lett. 63 (1989) 199--202. \bibitem{Gepner87b} D.~Gepner, New conformal field theories associated with {L}ie algebras and their partition functions, Nucl. Phys. B 290 (1987) 10. \bibitem{Wang06} Z.~Wang, Classification of {TQFT}s, talk at the {KITP} conference on {T}opological {P}hases and {Q}uantum {C}omputation, {S}anta {B}arbara (2006). \newline\urlprefix\url{http://online.itp.ucsb.edu/online/qubit\_c06/} \bibitem{Gepner94} D.~Gepner, A.~Kapustin, On the classification of fusion rings, Phys. Lett. B 349 (1995) 71--75, hep-th/9410089. \bibitem{Freeman69} I.~M. Freeman, Why is space three-dimensional?, Am. J. Phys. 37~(12) (1969) 1222--1224, based on {W. B\"{u}chel: ``Warum hat der Raum drei Dimensionen?,'' Physikalische Bl\"{a}tter 19, 12, pp. 547--549 (December 1963)}. \bibitem{Buchberger06} B.~Buchberger, An algorithm for finding the basis elements in the residue class ring modulo a zero dimensional polynomial ideal, Ph.D. thesis (2006). \bibitem{Buchberger98} B.~Buchberger, An algorithmic criterion for the solvability of algebraic systems of equations 251 (1998) 535--545. \end{thebibliography}