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On the stratification of a compact 3-manifold by the trajectory spaces of a Morse-Smale flow | | Imre Major
; | | Date: |
15 Dec 2001 | | Subject: | Geometric Topology; Algebraic Geometry; Differential Geometry MSC-class: 57N10 | math.GT math.AG math.DG | | Abstract: | 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. | | Source: | arXiv, math.GT/0201132 | | Services: | Forum | Review | PDF | Favorites | |
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