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dc.contributor.authorPendleton, Ian Alexander
dc.date.accessioned2019-10-15T15:30:02Z
dc.date.available2019-10-15T15:30:02Z
dc.date.issued2019-05-30
dc.identifier.otherPendleton_cornellgrad_0058F_11441
dc.identifier.otherhttp://dissertations.umi.com/cornellgrad:11441
dc.identifier.otherbibid: 11050314
dc.identifier.urihttps://hdl.handle.net/1813/67332
dc.description.abstractThis is a collection of algebraic topological results for toric origami manifolds, mostly in dimension 4. Using a known formula for the fundamental group of a compact orientable toric origami manifold, a list of all groups obtainable as the fundamental group of a compact orientable toric origami 4-manifold is given, along with example manifolds that realize them. The known fundamental group formula is generalized to compact non-orientable toric origami manifolds of all dimensions. The homology and cohomology groups of toric origami 4-manifolds are explicitly constructed with generators realized as embedded submanifolds, and the intersection form and cohomology ring are calculated.
dc.language.isoen_US
dc.rightsAttribution 4.0 International
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.subjectalgebraic topology
dc.subjecttoric origami
dc.subjecttoric symplectic
dc.subjectMathematics
dc.subjectsymplectic geometry
dc.titleThe Fundamental Group, Homology, and Cohomology of Toric Origami 4-Manifolds
dc.typedissertation or thesis
thesis.degree.disciplineMathematics
thesis.degree.grantorCornell University
thesis.degree.levelDoctor of Philosophy
thesis.degree.namePh.D., Mathematics
dc.contributor.chairHolm, Tara S.
dc.contributor.committeeMemberSjamaar, Reyer
dc.contributor.committeeMemberManning, Jason F.
dcterms.licensehttps://hdl.handle.net/1813/59810
dc.identifier.doihttps://doi.org/10.7298/4nc1-3039


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