2003/10/02 by Ursula Ludwig, Ludwig, Ursula
Computer Science · Mathematics · Physics and Astronomy · #37B30 #55N10 #57R70 #58A35 #FOS: Mathematics #Geometric Topology (math.GT) #Homotopy and Cohomology in Algebraic Topology #Quantum chaos and dynamical systems #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.math/0310019
openalex publication_date 2003/10/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Our objective is to develop a stratified Morse theory with tangential conditions. We define a continuous strata-wise smooth Morse function on an abstract stratified space by using control conditions and radiality assumptions on the gradient vector field. For critical points of a Morse function one can show that the local unstable set is a manifold and the local stable set is itself an abstract stratified space. We also give a normal form for the gradient dynamics in the neighborhood of critical points. For a stratified Morse pair which satisfies the generic Morse-Smale condition we can build the Morse-Witten complex and show that its homology is equivalent to the singular homology of the space.