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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.
Editora: 2012.
Dissertação: Thesis (Ph. D.)--Stanford University, 2012.
Edição/Formato   Tese/dissertação : Documento : Tese/dissertação : e-book   Arquivo de Computador : Inglês
Base de Dados:WorldCat
Resumo:
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  Ler mais...
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Detalhes

Tipo de Material: Documento, Tese/dissertação, Recurso Internet
Tipo de Documento: Recurso Internet, Arquivo de Computador
Todos os Autores / Contribuintes: Luís Miguel Pereira De Matos Geraldes Diogo; Y Eliashberg; Søren Galatius; Eleny Ionel; Stanford University. Department of Mathematics.
Número OCLC: 809038246
Notas: Submitted to the Department of Mathematics.
Descrição: 1 online resource.
Responsabilidade: Luís Miguel Pereira de Matos Geraldes Diogo.

Resumo:

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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