Homology, Homotopy and Applications
Volume 12 (2010)
An algorithm for low dimensional group homology
Pages: 27 – 37
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.
Group homology; experimental mathematics; l algebra; computationa; Hopf’s formula
2010 Mathematics Subject Classification