The Fundamental Group, Homology, and Cohomology of Toric Origami 4-Manifolds

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.

Name thesis:degree_name

Ph.D., Mathematics

Level thesis:degree_level

Doctor of Philosophy

Discipline thesis:degree_discipline

Mathematics

Grantor

Cornell University

Year dc:date.issued

2019

Author dc:creator

• Pendleton, Ian Alexander

Committee members dc:contributor.committeemember

• Sjamaar, Reyer
• Manning, Jason F.

• algebraic topology
• toric origami
• toric symplectic
• Mathematics
• symplectic geometry

Statement dc:rights

• Attribution 4.0 International

Licence dc:rights.uri

• https://creativecommons.org/licenses/by/4.0/

Language dc:language.iso

en_US

DOI

https://doi.org/10.7298/4nc1-3039

Dc Identifier Other

ProQuest Submission ID: 11441
ProQuest Publication ID: 13883378

OAI identifier oai:identifier

oai:ecommons.cornell.edu:1813/67332