Curvature, diameter, and quotient manifolds
| dc.creator | Totaro, Burt | |
| dc.date | 2002-09-13 | |
| dc.date.accessioned | 2026-07-07T04:50:51Z | |
| dc.date.available | 2026-07-07T04:50:51Z | |
| dc.description | Gromov showed that there is an upper bound on the Betti numbers of all closed Riemannian n-manifolds of nonnegative sectional curvature. Grove asked whether such manifolds (if simply connected) fall into only finitely many rational homotopy types. We give a negative answer, in fact in dimension 6, which is the smallest possible. We also give counterexamples to some related questions in dimensions 7 and 9, improving the original counterexamples by Fang and Rong which were in dimensions at least 22. | |
| dc.description | 12 pages | |
| dc.identifier | https://arxiv.org/abs/math/0209173 | |
| dc.identifier | http://arxiv.org/abs/math/0209173 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/64943 | |
| dc.subject | Differential Geometry | |
| dc.subject | Algebraic Topology | |
| dc.subject | 53C20 (Primary) 55P62 (Secondary) | |
| dc.title | Curvature, diameter, and quotient manifolds | |
| dc.type | text |