An algorithm for low dimensional group homology

Details An algorithm for low dimensional group homology An algorithm for low dimensional group homology

2009-01-18

arxiv.org/abs/0901.2610v3

Mathematics

Algebraic Topology

12 pages, requires algorithm and clrscode packages. Typos corrected

Scientific paper

Given a finitely presented group $G$, Hopf's formula expresses the second integral homology of $G$ in terms of generators and relators. We give an algorithm that exploits Hopf's formula to estimate $H_2(G;k)$, with coefficients in a finite field k, and give examples using $G=SL_2$ over specific rings of integers. These examples are related to a conjecture of Quillen.

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