Morse-Smale-Witten complex for gradient-like vector fields on stratified spaces. (English) Zbl 1131.58008

Chéniot, Denis (ed.) et al., Singularity theory. Proceedings of the 2005 Marseille singularity school and conference, CIRM, Marseille, France, January 24–February 25, 2005. Dedicated to Jean-Paul Brasselet on his 60th birthday. Singapore: World Scientific (ISBN 978-981-270-410-8/hbk). 683-713 (2007).
Author’s Abstract: The aim of this article is to generalise the notion of gradient-like vector fields to stratified spaces and to establish the associated Morse-Smale-Witten complex. The Morse-inequalities which relate the number of singular points of the vector field to the homology of the stratified space are a consequence of the existence of this complex.
For the entire collection see [Zbl 1111.14001].


58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
58A35 Stratified sets