Cohomology Of Contact Toric Manifolds And Hard Lefschetz Property Of Hamiltonian Gkm Manifolds
| dc.contributor.author | Luo, Shisen | en_US |
| dc.contributor.chair | Holm, Tara S. | en_US |
| dc.contributor.committeeMember | Sjamaar, Reyer | en_US |
| dc.contributor.committeeMember | Knutson, Allen | en_US |
| dc.date.accessioned | 2013-09-05T15:59:05Z | |
| dc.date.available | 2013-09-05T15:59:05Z | |
| dc.date.issued | 2013-05-26 | en_US |
| dc.description.abstract | This thesis consists of two parts. Each part solves a topological problem in equivariant symplectic geometry using combinatorial methods. The classification problem of sympletic toric manifolds was solved by Delzant [Del88] and their cohomology rings were later computed in various ways by Davis-Januskiewicz [DJ91] and Tolman-Weitsman [TW03]. Contact toric manifolds are the analogue of symplectic toric manifolds. The classification problem was solved by Lerman [Ler03a]. In the first part of the thesis, we compute the cohomology ring of contact toric manifolds utilizing techniques in [DJ91]. The equivariant cohomology of Hamiltonian GKM manifolds can be computed as the graph cohomology of their GKM graphs. The combinatorial properties of GKM graphs were studied by Guillemin and Zara [GZ99], [GZ01]. In the second part of this thesis, we study the graph cohomology for a more general class of graphs and prove many properties about it. The most interesting one of these is a weak version of the Hard Lefschetz Property (HLP). It was known that HLP always holds for K¨ hler manifolds, but generally may fail for symplectic manifolds. a Hamiltonian GKM manifolds are symplectic but generally not K¨ hler. Our result a provides a new class of manifolds for which a weak version of HLP holds. | en_US |
| dc.identifier.other | bibid: 8267632 | |
| dc.identifier.uri | https://hdl.handle.net/1813/34121 | |
| dc.language.iso | en_US | en_US |
| dc.title | Cohomology Of Contact Toric Manifolds And Hard Lefschetz Property Of Hamiltonian Gkm Manifolds | en_US |
| dc.type | dissertation or thesis | en_US |
| thesis.degree.discipline | Mathematics | |
| thesis.degree.grantor | Cornell University | en_US |
| thesis.degree.level | Doctor of Philosophy | |
| thesis.degree.name | Ph. D., Mathematics |
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