Stratified Morse Theory with Tangential Conditions

Details Stratified Morse Theory with Tangential Conditions Stratified Morse Theory with Tangential Conditions

2003-10-02

arxiv.org/abs/math/0310019v2

Mathematics

Geometric Topology

This paper has been withdrawn by the author. Part of this article has been published in revised form under the title "Morse-Sm

Scientific paper

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.

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