On the algorithmic construction of classifying spaces and the isomorphism problem for biautomatic groups

Details On the algorithmic construction of classifying spaces and the isomorphism problem for biautomatic groups On the algorithmic construction of classifying spaces and the isomorphism problem for biautomatic groups

2011-02-28

arxiv.org/abs/1102.5652v1

Mathematics

Geometric Topology

21 pages, 4 figures

Scientific paper

We show that the isomorphism problem is solvable in the class of central extensions of word-hyperbolic groups, and that the isomorphism problem for biautomatic groups reduces to that for biautomatic groups with finite centre. We describe an algorithm that, given an arbitrary finite presentation of an automatic group $\Gamma$, will construct explicit finite models for the skeleta of $K(\Gamma,1)$ and hence compute the integral homology and cohomology of $\Gamma$.

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