Quasi-isometry invariance of cohomological dimension. (English. Abridged French version) Zbl 0805.20043
Summary: The groups \(H^ n(G,RG)\) are quasi-isometry invariants for all rings \(R\) and groups \(G\) possessing a \(K(G,1)\) which has finitely many cells in dimensions at most \(n\). It follows that the cohomological dimension is a quasi-isometry invariant for groups \(G\) admitting a finite \(K(G,1)\) complex.
MSC:
| 20J05 | Homological methods in group theory |
| 20F65 | Geometric group theory |
| 57M05 | Fundamental group, presentations, free differential calculus |
| 20F05 | Generators, relations, and presentations of groups |
| 16S34 | Group rings |
