The Fundamental Group, Homology, and Cohomology of Toric Origami 4-Manifolds
| dc.contributor.author | Pendleton, Ian Alexander | |
| dc.contributor.chair | Holm, Tara S. | |
| dc.contributor.committeeMember | Sjamaar, Reyer | |
| dc.contributor.committeeMember | Manning, Jason F. | |
| dc.date.accessioned | 2019-10-15T15:30:02Z | |
| dc.date.available | 2019-10-15T15:30:02Z | |
| dc.date.issued | 2019-05-30 | |
| dc.description.abstract | This 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.identifier.doi | https://doi.org/10.7298/4nc1-3039 | |
| dc.identifier.other | Pendleton_cornellgrad_0058F_11441 | |
| dc.identifier.other | http://dissertations.umi.com/cornellgrad:11441 | |
| dc.identifier.other | bibid: 11050314 | |
| dc.identifier.uri | https://hdl.handle.net/1813/67332 | |
| dc.language.iso | en_US | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.subject | algebraic topology | |
| dc.subject | toric origami | |
| dc.subject | toric symplectic | |
| dc.subject | Mathematics | |
| dc.subject | symplectic geometry | |
| dc.title | The Fundamental Group, Homology, and Cohomology of Toric Origami 4-Manifolds | |
| dc.type | dissertation or thesis | |
| dcterms.license | https://hdl.handle.net/1813/59810 | |
| thesis.degree.discipline | Mathematics | |
| thesis.degree.grantor | Cornell University | |
| thesis.degree.level | Doctor of Philosophy | |
| thesis.degree.name | Ph.D., Mathematics |
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