In mathematics, stratified Morse theory is an analogue to
Morse theory for general
stratified spaces, originally developed by
Mark Goresky and
Robert MacPherson. The main point of the theory is to consider functions
and consider how the stratified space
changes as the real number
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.
See also
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Digital Morse theory In mathematics, digital Morse theory is a digital adaptation of continuum Morse theory for scalar volume data. This is not about the Samuel Morse's Morse code of long and short clicks or tones used in manual electric telegraphy. The term was fir ...
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Discrete Morse theory
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Level-set method
References
DJVU file on Goresky's page
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Generalized manifolds
Morse theory
Singularity theory
Stratifications
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