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The topology of spaces of J-holomorphic maps to CP2

Author: Jeremy Kenneth Miller; Ralph L Cohen; Søren Galatius; Eleny Ionel; Stanford University. Department of Mathematics.
Publisher: 2012.
Dissertation: Thesis (Ph. D.)--Stanford University, 2012.
Edition/Format:   Thesis/dissertation : Document : Thesis/dissertation : eBook   Computer File : English
Database:WorldCat
Summary:
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  Read more...
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Details

Material Type: Document, Thesis/dissertation, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Jeremy Kenneth Miller; Ralph L Cohen; Søren Galatius; Eleny Ionel; Stanford University. Department of Mathematics.
OCLC Number: 806217205
Notes: Submitted to the Department of Mathematics.
Description: 1 online resource.
Responsibility: Jeremy Kenneth Miller.

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]).

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