On
the algorithmic construction of classifying spaces and
the isomorphism problem for biautomatic groups
Martin R. Bridson and Lawrence Reeves
Final version sent to journal on 28 Feb 2011; to appear
in the volume for 60th birthday of Fabrizio Catanese.
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 $\Gamma$.