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Filtered floer and symplectic homology via Gromov-Witten theory

Autor Luís Miguel Pereira De Matos Geraldes Diogo; Y Eliashberg; Søren Galatius; Eleny Ionel; Stanford University. Department of Mathematics.
Vydavatel: 2012.
Dizertace: Thesis (Ph. D.)--Stanford University, 2012.
Vydání/formát:   Kvalifikační práce : Document : Thesis/dissertation : e-kniha   Computer File : English
Databáze:WorldCat
Shrnutí:
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  Přečíst více...
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Detaily

Typ materiálu: Document, Thesis/dissertation, Internetový zdroj
Typ dokumentu: Internet Resource, Computer File
Všichni autoři/tvůrci: Luís Miguel Pereira De Matos Geraldes Diogo; Y Eliashberg; Søren Galatius; Eleny Ionel; Stanford University. Department of Mathematics.
OCLC číslo: 809038246
Poznámky: Submitted to the Department of Mathematics.
Popis: 1 online resource.
Odpovědnost: Luís Miguel Pereira de Matos Geraldes Diogo.

Anotace:

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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