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An Introduction to Discrete Morse Theory

open access: yes, 2022
Vi presenterer en introduksjon til diskret Morse teori, hvor vi starter med å definere simplisialkomplekser og fortsetter med diskrete Morse-funksjoner og induserte gradientvektorfelt. Vi lærer hvordan vi lager den ene fra den andre og hvordan de hjelper oss å lære om simplisiell homologi og å sammenligne forskjellige simplisialkomplekser.
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Topological data analysis and topological deep learning beyond persistent homology: a review. [PDF]

open access: yesArtif Intell Rev
Su Z   +7 more
europepmc   +1 more source

Generalizations of discrete Morse theory

open access: yes, 2017
We generalize Forman’s discrete Morse theory, on one end by developing a discrete analogue of Morse-Bott theory for CW complexes, motivated by Morse-Bott theory in the smooth setting. On the other, motivated by J-N. Corvellec’s Morse theory for continuous functionals, we generalize Forman’s discrete Morse-floer theory by considering a vector field more
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