The Morse Complex for a Morse Function on a Manifold with Corners
| dc.creator | Handron, David G. C. | |
| dc.date | 2004-06-23 | |
| dc.date | 2004-08-12 | |
| dc.date.accessioned | 2026-07-07T05:09:32Z | |
| dc.date.available | 2026-07-07T05:09:32Z | |
| dc.description | A Morse function f on a manifold with corners M allows the characterization of the Morse data for a critical point by the Morse index. In fact, a modified gradient flow allows a proof of the Morse theorems in a manner similar to that of classical Morse theory. It follows that M is homotopy equivalent to a CW-complex with one cell of dimension λfor each essential critical point of index λ. The goal of this article is to determine the boundary maps of this CW-complex, in the case where M is compact and orientable. First, the boundary maps are defined in terms of the modified gradient flow. Then a transversality condition is imposed which insures that the attaching map is non-degenerate in a neighborhood of each critical point. The degree of this map is then interpreted as a sum of trajectories connecting two critical points each counted with a multiplicity determined by a choice of orientations on the tangent spaces of the unstable manifold at each critical point. | |
| dc.description | 17 pages, 0 figures updated and clarified definitions, particularly in Section 1.1 (Setup and Definitions) and Definion 5 (in this version) of a Morse-Smale function | |
| dc.identifier | https://arxiv.org/abs/math/0406486 | |
| dc.identifier | http://arxiv.org/abs/math/0406486 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/71658 | |
| dc.subject | Geometric Topology | |
| dc.subject | 57R70, 57R25 | |
| dc.title | The Morse Complex for a Morse Function on a Manifold with Corners | |
| dc.type | text |