Homological Invariants and Quasi-Isometry
| dc.creator | Sauer, Roman | |
| dc.date | 2003-12-05 | |
| dc.date | 2004-10-18 | |
| dc.date.accessioned | 2026-07-07T05:03:36Z | |
| dc.date.available | 2026-07-07T05:03:36Z | |
| dc.description | Building upon work of Y. Shalom we give a homological-algebra flavored definition of an induction map in group homology associated to a topological coupling. As an application we obtain estimates of the (co)homological dimension of groups G and H, where G embeds uniformly into H and the (co)homological dimension of G is finite. Another consequence of our results is that the Hirsch ranks of quasi-isometric solvable groups coincide. Further, it is shown that the real cohomology rings of quasi-isometric nilpotent groups are isomorphic as graded rings. On the analytic side, we apply the induction technique to Novikov-Shubin invariants of amenable groups, which can be seen as homological invariants, and show their invariance under quasi-isometry. | |
| dc.description | 33 pages; v2: major extension and change of v1 which contained only the result about Novikov-Shubin invariants | |
| dc.identifier | https://arxiv.org/abs/math/0312129 | |
| dc.identifier | http://arxiv.org/abs/math/0312129 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69488 | |
| dc.subject | Algebraic Topology | |
| dc.subject | Group Theory | |
| dc.subject | 20F65 (Primary) 20F16 (Secondary) | |
| dc.title | Homological Invariants and Quasi-Isometry | |
| dc.type | text |