On the stratification of a compact 3-manifold by the trajectory spaces of a Morse-Smale flow
| dc.creator | Major, Imre | |
| dc.date | 2002-01-15 | |
| dc.date.accessioned | 2026-07-07T04:45:52Z | |
| dc.date.available | 2026-07-07T04:45:52Z | |
| dc.description | We consider a Morse function $f$ and a Morse-Smale gradient-like vector field $X$ on a compact connected oriented 3-manifold $M$ such that $f$ has only one critical point of index 3. Based on Laudenbach's ideas, we will show that the flow of $X$ can be isotoped into one so that the trajectory spaces of the new flow provide a stratification for $M$. We will construct "natural" tubular neighborhoods about each given trajectory space of the new flow such that these neighborhoods are stratified by open subsets of trajectory spaces that co-bound the given one. In connection with this we introduce the concept of {\it conic stratification} of a manifold and point out that this is the appropriate condition the stratification of $M$ by trajectory spaces should be required to satisfy. | |
| dc.description | 21 pages | |
| dc.identifier | https://arxiv.org/abs/math/0201132 | |
| dc.identifier | http://arxiv.org/abs/math/0201132 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/63117 | |
| dc.subject | Geometric Topology | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Differential Geometry | |
| dc.subject | 57N10 | |
| dc.title | On the stratification of a compact 3-manifold by the trajectory spaces of a Morse-Smale flow | |
| dc.type | text |