Central Extensions of Word Hyperbolic Groups

Walter Neumann; Lawrence Reeves

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Central Extensions of Word Hyperbolic Groups

Walter Neumann·Lawrence Reeves

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Abstract

Thurston has claimed (unpublished) that central extensions of word hyperbolic groups by finitely generated abelian groups are automatic. We show that they are in fact biautomatic. Further, we show that every 2-dimensional cohomology class on a word hyperbolic group can be represented by a bounded 2-cocycle. This lends weight to the claim of Gromov that for a word hyperbolic group, the cohomology in every dimension is bounded.

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Walter Neumann, Lawrence Reeves. 1995-07-13. Central Extensions of Word Hyperbolic Groups. https://arxiv.org/abs/math/9507201

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