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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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