English

An algorithm for low dimensional group homology

Algebraic Topology 2012-11-13 v3 K-Theory and Homology

Abstract

Given a finitely presented group GG, Hopf's formula expresses the second integral homology of GG in terms of generators and relators. We give an algorithm that exploits Hopf's formula to estimate H2(G;k)H_2(G;k), with coefficients in a finite field k, and give examples using G=SL2G=SL_2 over specific rings of integers. These examples are related to a conjecture of Quillen.

Keywords

Cite

@article{arxiv.0901.2610,
  title  = {An algorithm for low dimensional group homology},
  author = {Joshua Roberts},
  journal= {arXiv preprint arXiv:0901.2610},
  year   = {2012}
}

Comments

12 pages, requires algorithm and clrscode packages. Typos corrected

R2 v1 2026-06-21T12:01:58.389Z