The topology of spaces of J-holomorphic maps to CP²
Abstract/Contents
- Abstract
- In [Seg79], Graeme Segal proved that the space of holomorphic maps from a Riemann surface to a complex projective space is homology equivalent to the corresponding continuous mapping space through a range of dimensions increasing with degree. I will address if a similar result holds when other almost complex structures are put on projective space. For any compatible almost complex structure J on CP^2, I prove that the inclusion map from the space of J-holomorphic maps to the space of continuous maps induces a homology surjection through a range of dimensions tending to infinity with degree. The proof involves comparing the scanning map of topological chiral homology ([Sal01], [Lur09], [And10]) with gluing of J-holomorphic curves ([MS94], [Sik03]).
Description
| Type of resource | text |
|---|---|
| Form | electronic; electronic resource; remote |
| Extent | 1 online resource. |
| Publication date | 2012 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Associated with | Miller, Jeremy Kenneth |
|---|---|
| Associated with | Stanford University, Department of Mathematics |
| Primary advisor | Cohen, Ralph L, 1952- |
| Thesis advisor | Cohen, Ralph L, 1952- |
| Thesis advisor | Galatius, Søren, 1976- |
| Thesis advisor | Ionel, Eleny |
| Advisor | Galatius, Søren, 1976- |
| Advisor | Ionel, Eleny |
Subjects
| Genre | Theses |
|---|
Bibliographic information
| Statement of responsibility | Jeremy Kenneth Miller. |
|---|---|
| Note | Submitted to the Department of Mathematics. |
| Thesis | Thesis (Ph.D.)--Stanford University, 2012. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2012 by Jeremy Kenneth Miller
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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