On the stratification of a compact 3-manifold by the trajectory spaces of a Morse-Smale flow

dc.creatorMajor, Imre
dc.date2002-01-15
dc.date.accessioned2026-07-07T04:45:52Z
dc.date.available2026-07-07T04:45:52Z
dc.descriptionWe 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.description21 pages
dc.identifierhttps://arxiv.org/abs/math/0201132
dc.identifierhttp://arxiv.org/abs/math/0201132
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/63117
dc.subjectGeometric Topology
dc.subjectAlgebraic Geometry
dc.subjectDifferential Geometry
dc.subject57N10
dc.titleOn the stratification of a compact 3-manifold by the trajectory spaces of a Morse-Smale flow
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