An algorithm for low dimensional group homology

Abstract

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 $G=S{L}_2$ over specific rings of integers. These examples are related to a conjecture of Quillen.

12 pages, requires algorithm and clrscode packages. Typos corrected