Homology, Homotopy and Applications

Volume 12 (2010)

Number 1

An algorithm for low dimensional group homology

Pages: 27 – 37

DOI: https://dx.doi.org/10.4310/HHA.2010.v12.n1.a3

Author

Joshua Roberts (Department of Mathematics, University of Kentucky, Lexington, Ky., U.S.A.)

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 $G=SL_2$ over specific rings of integers. These examples are related to a conjecture of Quillen.

Keywords

Group homology, experimental mathematics, l algebra, computationa, Hopf’s formula

2010 Mathematics Subject Classification

20G30, 20J06

Full Text (PDF format)

Published 1 January 2010

Supplemental file: GAP code (text)