The Fundamental Group, Homology, and Cohomology of Toric Origami 4-Manifolds
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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.
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2019-05-30
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algebraic topology; toric origami; toric symplectic; Mathematics; symplectic geometry
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Holm, Tara S.
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Sjamaar, Reyer
Manning, Jason F.
Manning, Jason F.
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Mathematics
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Ph.D., Mathematics
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Doctor of Philosophy
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Government Document
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Attribution 4.0 International
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dissertation or thesis