An algorithm for low dimensional group homology

Joshua Roberts

doi:hha/1296223819

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Home > Journals > Homology Homotopy Appl. > Volume 12 > Issue 1 > Article

2010 An algorithm for low dimensional group homology

Joshua Roberts

Homology Homotopy Appl. 12(1): 27-37 (2010).

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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 H2(G;k), with coefficients in a finite field k, and give examples using G=SL2 over specific rings of integers. These examples are related to a conjecture of Quillen.