2026-09-20T14:07:51Zhttps://ecommons.cornell.edu/server/oai/requestoai:ecommons.cornell.edu:1813/673322026-05-15T19:47:53Zcom_1813_35col_1813_47
Pendleton, Ian Alexander
Holm, Tara S.
Sjamaar, Reyer
Manning, Jason F.
2019-10-15T15:30:02Z
2019-10-15T15:30:02Z
2019-05-30
ProQuest Submission ID: 11441
ProQuest Publication ID: 13883378
https://hdl.handle.net/1813/67332
https://doi.org/10.7298/4nc1-3039
11050314
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.
en_US
Attribution 4.0 International
https://creativecommons.org/licenses/by/4.0/
algebraic topology
toric origami
toric symplectic
Mathematics
symplectic geometry
The Fundamental Group, Homology, and Cohomology of Toric Origami 4-Manifolds
dissertation or thesis
application/pdf
Mathematics
Cornell University
Doctor of Philosophy
Ph.D., Mathematics
https://hdl.handle.net/1813/59810
Publication
Cornell Theses and Dissertations
Pendleton, Ian Alexander
5893a6ea-7af3-41d7-abc6-04bcd26ab5df
open.access
open.access
<Publication xmlns="https://www.openaire.eu/cerif-profile/1.1/" id="05e1a0cc-c21b-44b8-a055-a2188a22b6fe">
<Type xmlns="https://www.openaire.eu/cerif-profile/vocab/COAR_Publication_Types">http://purl.org/coar/resource_type/c_1843</Type>
<Language>en_US</Language>
<Title>The Fundamental Group, Homology, and Cohomology of Toric Origami 4-Manifolds</Title>
<PublishedIn>
<Publication>
</Publication>
</PublishedIn>
<PublicationDate>2019-05-30</PublicationDate>
<DOI>https://doi.org/10.7298/4nc1-3039</DOI>
<Authors>
<Author>
<DisplayName>Pendleton, Ian Alexander</DisplayName>
<Affiliation>
<OrgUnit>
</OrgUnit>
</Affiliation>
</Author>
</Authors>
<Editors>
</Editors>
<Publishers>
<Publisher>
<OrgUnit />
</Publisher>
</Publishers>
<License>https://creativecommons.org/licenses/by/4.0/</License>
<Keyword>algebraic topology</Keyword>
<Keyword>toric origami</Keyword>
<Keyword>toric symplectic</Keyword>
<Keyword>Mathematics</Keyword>
<Keyword>symplectic geometry</Keyword>
<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.</Abstract>
<Access xmlns="http://purl.org/coar/access_right"
>
</Access>
</Publication>