Topological rigidity for non-aspherical manifolds
| dc.creator | Kreck, Matthias | |
| dc.creator | Lueck, Wolfgang | |
| dc.date | 2005-09-11 | |
| dc.date.accessioned | 2026-07-07T05:23:07Z | |
| dc.date.available | 2026-07-07T05:23:07Z | |
| dc.description | The Borel Conjecture predicts that closed aspherical manifolds are topological rigid. We want to investigate when a non-aspherical oriented connected closed manifold M is topological rigid in the following sense. If f: N --> M is an orientation preserving homotopy equivalence with a closed oriented manifold as target, then there is an orientation preserving homeomorphism h: N --> M such that h and f induce up to conjugation the same maps on the fundamental groups. We call such manifolds Borel manifolds. We give partial answers to this questions for S^k x S^d, for sphere bundles over aspherical closed manifolds of dimension less or equal to 3 and for 3-manifolds with torsionfree fundamental groups. We show that this rigidity is inherited under connected sums in dimensions greater or equal to 5. We also classify manifolds of dimension 5 or 6 whose fundamental group is the one of a surface and whose second homotopy group is trivial. | |
| dc.description | 35 pages | |
| dc.identifier | https://arxiv.org/abs/math/0509238 | |
| dc.identifier | http://arxiv.org/abs/math/0509238 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/76311 | |
| dc.subject | Geometric Topology | |
| dc.subject | 57N99,; 57R67 | |
| dc.title | Topological rigidity for non-aspherical manifolds | |
| dc.type | text |