Homological Decision

W. A. Bogley and J. Harlander, Homological decisions problems for finitely generated groups with solvable word problem, to appear in IJAC.

Abstract

We show that for finitely generated groups $P$ with solvable word problem, there is no algorithm to determine whether $H_1(P)$ is trivial, nor whether $H_2(P)$ is trivial.

AMS Subject classification: Primary 20F10, Secondary 20J06.

Keywords: homology of groups, word problem