2002/01/15 by Imre Major, Major, Imre
Computer Science · Mathematics · #57N10 #Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Topological and Geometric Data Analysis #math.AG #math.DG #math.GT #msc:57N10
paper · pdf · doi:10.48550/arxiv.math/0201132
21 pages
arxiv created 2002/01/15 · openalex publication_date 2002/01/15 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.