A Generalization of Surgery to Cellular Complexes

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dc.contributor.advisorLoft, Brian
dc.creatorGueli, Ryan John
dc.date.accessioned2018-04-26T18:12:34Z
dc.date.available2018-04-26T18:12:34Z
dc.date.created2018-05
dc.date.issued2018-04-12
dc.date.submittedMay 2018
dc.date.updated2018-04-26T18:13:06Z
dc.description.abstractIn the 1990s Robin Forman carefully generalized Morse theory to cellular complexes. In this thesis we are concerned with the connection Morse theory provides in surgery theory. There exists a theorem linking surgery on embedded spheres to cobordisms whose proof relies on smooth Morse theory. Therefore, we examine if a similar theorem exists on cellular complexes whose proof relies on discrete Morse theory. In order to accomplish this we will provide a way to perform surgery on cellular complexes as well as a possibility for defining cellular cobordism.
dc.format.mimetypeapplication/pdf
dc.identifier.urihttp://hdl.handle.net/20.500.11875/2353
dc.language.isoen
dc.subjectDifferential Geometry
dc.subjectSmooth Morse Theory
dc.subjectDiscrete Morse Theory
dc.subjectSurgery
dc.subjectCobordism
dc.subjectCellular Surgery
dc.subjectLocally Cellular Cobordant.
dc.titleA Generalization of Surgery to Cellular Complexes
dc.typeThesis
dc.type.materialtext
thesis.degree.departmentMathematics & Statistics
thesis.degree.grantorSam Houston State University
thesis.degree.levelMasters
thesis.degree.nameMaster of Science

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