Combable groups have group cohomology of polynomial growth. (English) Zbl 1167.20028
Summary: 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.
MSC:
20J06 | Cohomology of groups |
20F65 | Geometric group theory |
18G60 | Other (co)homology theories (MSC2010) |
20F05 | Generators, relations, and presentations of groups |