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Combable groups have group cohomology of polynomial growth

Ralf Meyer
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Abstract

Group cohomology of polynomial growth is defined for any finitely generated discrete group, using cochains that have polynomial growth with respect to the word length function. We give a geometric condition that guarantees that it agrees with the usual group cohomology and verify this condition for a class of combable groups. Our condition involves a chain complex that is closely related to exotic cohomology theories studied by Allcock and Gersten and by Mineyev.

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Ralf Meyer. 2004-10-28. Combable groups have group cohomology of polynomial growth. https://doi.org/10.1093/qmath/hai003

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