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In mathematics, '''stratified Morse theory''' is an analogue to [[Morse theory]] for general [[topologically stratified space|stratified spaces]], originally developed by [[Mark Goresky]] and [[Robert MacPherson (mathematician)|Robert MacPherson]]. The main point of the theory is to consider functions <math>f : M \to \mathbb R</math> and consider how the stratified space <math>f^{-1}(-\infty,c]</math> changes as the real number <math>c \in \mathbb R</math> changes. Morse theory of stratified spaces has uses everywhere from pure mathematics topics such as braid groups and [[Lawrence-Krammer representation|representations]] to robot motion planning and potential theory. A popular application in pure mathematics is Morse theory on manifolds with boundary, and manifolds with corners.
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==See also==
 
* [[Digital Morse theory]]
* [[Discrete Morse theory]]
* [[Morse theory]]
* [[Level set method]]
 
==References==
* "Stratified Morse theory", by M. Goresky and R. MacPherson Springer-Verlag, Berlin, Heidelberg, New York, 1988, xiv + 272 pp. [http://www.math.ias.edu/~goresky/pdf/SMT.djvu DJVU file on Goresky's page]
* D. Handron, Generalized billiard paths and Morse theory on manifolds with corners. Topology and its Applications, Volume 126, Number 1, 30 November 2002, pp.&nbsp;83&ndash;118(36)
* S.A. Vakhrameev, Morse lemmas for smooth functions on manifolds with corners. Dynamical systems, 8. J. Math. Sci. (New York) 100 (2000), no. 4, 2428&ndash;2445.
 
[[Category:Singularity theory]]
[[Category:Generalized manifolds]]
[[Category:Morse theory]]
 
{{topology-stub}}

Latest revision as of 13:32, 21 July 2014

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