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Generalizations of discrete Morse theory

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 general than the one extracted from a discrete Morse function, and defining a boundary operator from which the Betti numbers of the CW complex are obtained. We also do some Conley theory analysis.

Identiferoai:union.ndltd.org:DRESDEN/oai:qucosa:de:qucosa:17104
Date02 February 2018
CreatorsYaptieu Djeungue, Odette Sylvia
ContributorsUniversität Leipzig
Source SetsHochschulschriftenserver (HSSS) der SLUB Dresden
LanguageEnglish
Detected LanguageEnglish
Typeinfo:eu-repo/semantics/acceptedVersion, doc-type:doctoralThesis, info:eu-repo/semantics/doctoralThesis, doc-type:Text
Rightsinfo:eu-repo/semantics/openAccess

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