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A generating function of the number of homomorphisms from a surface group into a finite group

Motohico Mulase·Josephine T. Yu
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Abstract

A generating function of the number of homomorphisms from the fundamental group of a compact oriented or non-orientable surface without boundary into a finite group is obtained in terms of an integral over a real group algebra. We calculate the number of homomorphisms using the decomposition of the group algebra into irreducible factors. This gives a new proof of the classical formulas of Frobenius, Schur, and Mednykh.

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BibTeXRIS

Motohico Mulase, Josephine T. Yu. 2002-11-07. A generating function of the number of homomorphisms from a surface group into a finite group. https://arxiv.org/abs/math/0209008

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