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.
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa:de:qucosa:17104 |
| Date | 02 February 2018 |
| Creators | Yaptieu Djeungue, Odette Sylvia |
| Contributors | Universität Leipzig |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | English |
| Detected Language | English |
| Type | info:eu-repo/semantics/acceptedVersion, doc-type:doctoralThesis, info:eu-repo/semantics/doctoralThesis, doc-type:Text |
| Rights | info:eu-repo/semantics/openAccess |
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