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Filtered floer and symplectic homology via Gromov-Witten theory

Author: Luís Miguel Pereira De Matos Geraldes Diogo; Y Eliashberg; 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:
We describe a procedure for computing Floer and symplectic homology groups, with action filtration and algebraic operations, in a class of examples. Namely, we consider closed monotone symplectic manifolds with smooth symplectic divisors, Poincaré dual to a positive multiple of the symplectic form. We express the Floer homology of the manifold and the symplectic homology of the complement of the divisor, for a  Read more...
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Details

Material Type: Document, Thesis/dissertation, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Luís Miguel Pereira De Matos Geraldes Diogo; Y Eliashberg; Søren Galatius; Eleny Ionel; Stanford University. Department of Mathematics.
OCLC Number: 809038246
Notes: Submitted to the Department of Mathematics.
Description: 1 online resource.
Responsibility: Luís Miguel Pereira de Matos Geraldes Diogo.

Abstract:

We describe a procedure for computing Floer and symplectic homology groups, with action filtration and algebraic operations, in a class of examples. Namely, we consider closed monotone symplectic manifolds with smooth symplectic divisors, Poincaré dual to a positive multiple of the symplectic form. We express the Floer homology of the manifold and the symplectic homology of the complement of the divisor, for a special class of Hamiltonians, in terms of absolute and relative Gromov--Witten invariants, and some additional Morse-theoretic information. As an application, we compute the symplectic homology rings of cotangent bundles of spheres, and compare our results with an earlier computation in string topology.

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