MiS Preprint Repository

Delve into the future of research at MiS with our preprint repository. Our scientists are making groundbreaking discoveries and sharing their latest findings before they are published. Explore repository to stay up-to-date on the newest developments and breakthroughs.

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.

Oct 2, 2003
Oct 2, 2003
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