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Filtered floer and symplectic homology via Gromov-Witten theory Titelvorschau
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Filtered floer and symplectic homology via Gromov-Witten theory

Verfasser/in: Luís Miguel Pereira De Matos Geraldes Diogo; Y Eliashberg; Søren Galatius; Eleny Ionel; Stanford University. Department of Mathematics.
Verlag: 2012.
Dissertation: Thesis (Ph. D.)--Stanford University, 2012.
Ausgabe/Format   Diplomarbeit/Dissertation : Dokument : Diplomarbeit/Dissertation : E-Book   Computer-Datei : Englisch
Datenbank:WorldCat
Zusammenfassung:
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  Weiterlesen…
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Details

Medientyp: Dokument, Diplomarbeit/Dissertation, Internetquelle
Dokumenttyp: Internet-Ressource, Computer-Datei
Alle Autoren: Luís Miguel Pereira De Matos Geraldes Diogo; Y Eliashberg; Søren Galatius; Eleny Ionel; Stanford University. Department of Mathematics.
OCLC-Nummer: 809038246
Anmerkungen: Submitted to the Department of Mathematics.
Beschreibung: 1 online resource.
Verfasserangabe: 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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