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MiS Preprint

Stratified Morse Theory with Tangential Conditions

Ursula Ludwig


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.

MSC Codes:
58A35, 37B30, 57R70, 55N10
stratified sets, morse-conley indices, critical points and critical submanifolds, singular homology theory

Related publications

2003 Repository Open Access
Ursula Ludwig

Stratified morse theory with tangential conditions