Holomorphic curve invariants of open contact manifolds
Abstract/Contents
- Abstract
- Contact homology is a well-established tool for studying contact manifolds. It was originally defined for closed manifolds, and variants have been produced for a certain class of open manifolds, but these depend on certain extra structure at infinity, and hence do not provide an invariant for the manifold itself. In this thesis, we introduce a variant of contact homology which is defined for certain ("convex") open manifolds. This provides the first tool for distinguishing tight contact structures on euclidean space and, as an application, we prove the existence of exotic tight contact structures on (4m+1)-dimensional euclidean space for every m> 0. In addition, we give a preliminary version of a general framework for defining algebraic invariants based on holomorphic curves.
Description
| Type of resource | text |
|---|---|
| Form | electronic resource; remote; computer; online resource |
| Extent | 1 online resource. |
| Place | California |
| Place | [Stanford, California] |
| Publisher | [Stanford University] |
| Copyright date | 2021; ©2021 |
| Publication date | 2021; 2021 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Author | Helfer, Joseph Albert |
|---|---|
| Degree supervisor | Eliashberg, Y, 1946- |
| Thesis advisor | Eliashberg, Y, 1946- |
| Thesis advisor | Ionel, Eleny |
| Thesis advisor | Manolescu, Ciprian, 1978- |
| Degree committee member | Ionel, Eleny |
| Degree committee member | Manolescu, Ciprian, 1978- |
| Associated with | Stanford University, Department of Mathematics |
Subjects
| Genre | Theses |
|---|---|
| Genre | Text |
Bibliographic information
| Statement of responsibility | Joseph Helfer. |
|---|---|
| Note | Submitted to the Department of Mathematics. |
| Thesis | Thesis Ph.D. Stanford University 2021. |
| Location | https://purl.stanford.edu/sf528sy1627 |
Access conditions
- Copyright
- © 2021 by Joseph Albert Helfer
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