Mednykh's Formula via Lattice Topological Quantum Field Theories
| dc.creator | Snyder, Noah | |
| dc.date | 2007-03-05 | |
| dc.date | 2008-08-28 | |
| dc.date.accessioned | 2026-07-07T09:58:47Z | |
| dc.date.available | 2026-07-07T09:58:47Z | |
| dc.description | Mednykh proved that for any finite group G and any orientable surface S, there is a formula for #Hom(pi_1(S), G) in terms of the Euler characteristic of S and the dimensions of the irreducible representations of G. A similar formula in the nonorientable case was proved by Frobenius and Schur. Both of these proofs use character theory and an explicit presentation for π_1. These results have been reproven using quantum field theory. Here we present a greatly simplified proof of these results which uses only elementary topology and combinatorics. The main tool is an elementary invariant of surfaces attached to a semisimple algebra called a lattice topological quantum field theory. | |
| dc.description | 11 pages, 6 figures. v3 clarifies the dicussion of the Frobenius-Schur indicators and improves the argument in the quaternionic case | |
| dc.identifier | https://arxiv.org/abs/math/0703073 | |
| dc.identifier | http://arxiv.org/abs/math/0703073 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/167845 | |
| dc.subject | Quantum Algebra | |
| dc.subject | Geometric Topology | |
| dc.subject | 57R56; 20C05 | |
| dc.title | Mednykh's Formula via Lattice Topological Quantum Field Theories | |
| dc.type | text |