On Complexes Equivalent to $\mathbb{S}^3$-bundles over $\mathbb{S}^4$
| dc.creator | Kitchloo, Nitu | |
| dc.creator | Shankar, Krishnan | |
| dc.date | 2000-04-03 | |
| dc.date.accessioned | 2026-07-07T04:34:36Z | |
| dc.date.available | 2026-07-07T04:34:36Z | |
| dc.description | There has been renewed interest in $\mathbb{S}^3$-bundles over $\mathbb{S}^4$ since K. Grove and W. Ziller constructed metrics on nonnegative curvature on the total spaces of these bundles. In this paper we write down necessary and sufficient conditions for a CW complex to be homotopy equivalent to such a bundle. We also show that for a manifold homotopy equivalent to such a bundle, in certain cases, there is no obstruction to homeomorphism. We use this to show that the Berger manifold, $\text{Sp}(2)/\text{Sp}(1)$, is PL-homeomorphic to such a bundle. This question was raised in the paper by Grove and Ziller since this manifold, which admits a normal homogeneous metric of positive sectional curvature, has the cohomology ring of such a bundle. The principal technique used is the study of the Serre spectral sequence of various fibrations. | |
| dc.description | 12 pages, no figures | |
| dc.identifier | https://arxiv.org/abs/math/0004013 | |
| dc.identifier | http://arxiv.org/abs/math/0004013 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/58967 | |
| dc.subject | Algebraic Topology | |
| dc.subject | Differential Geometry | |
| dc.subject | 55R15; 55R40; 57T35 | |
| dc.title | On Complexes Equivalent to $\mathbb{S}^3$-bundles over $\mathbb{S}^4$ | |
| dc.type | text |