Geometric Diffeomorphism Finiteness in Low Dimensions and Homotopy Group Finiteness
| dc.creator | Tuschmann, Wilderich | |
| dc.date | 1999-08-29 | |
| dc.date.accessioned | 2026-07-07T05:30:33Z | |
| dc.date.available | 2026-07-07T05:30:33Z | |
| dc.description | Our main result asserts that for any given numbers C and D the class of simply connected closed smooth manifolds of dimension m<7 which admit a Riemannian metric with sectional curvature bounded in absolute value by C and diameter uniformly bounded from above by D contains only finitely many diffeomorphism types. Thus in these dimensions the lower positive bound on volume in Cheeger's Finiteness Theorem can be replaced by a purely topological condition, simply-connectedness. In dimension 4 instead of simply-connectedness here only non-vanishing of the Euler characteristic has to be required. As a topological corollary we obtain that for k+l<7 there are over a given smooth closed l-manifold only finitely many principal $T^k$ bundles with simply connected and non-diffeomorphic total spaces. Furthermore, for any given numbers C and D and any dimension m it is shown that for each natural number i there are up to isomorphism always only finitely many possibilities for the i-th homotopy group of a simply connected closed m-manifold which admits a metric with sectional curvature bounded in absolute value by C and diameter bounded from above by D. | |
| dc.description | AMS-TeX, 4 pages | |
| dc.identifier | https://arxiv.org/abs/math/9908156 | |
| dc.identifier | http://arxiv.org/abs/math/9908156 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/79025 | |
| dc.subject | Differential Geometry | |
| dc.subject | Geometric Topology | |
| dc.subject | 53C20 | |
| dc.title | Geometric Diffeomorphism Finiteness in Low Dimensions and Homotopy Group Finiteness | |
| dc.type | text |