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 |
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Form | electronic; electronic resource; remote |
Extent | 1 online resource. |
Publication date | 2012 |
Issuance | monographic |
Language | English |
Creators/Contributors
Associated with | Miller, Jeremy Kenneth | |
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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 |
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Bibliographic information
Statement of responsibility | Jeremy Kenneth Miller. |
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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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