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An
open string analogue of Viterbo functoriality
Mohammed Abouzaid and Paul Seidel |
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Geometry & Topology 14 (2010) 627–718
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Abstract |
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Liouville domains are a special type of symplectic manifolds with boundary (they have an everywhere defined Liouville flow, pointing outwards along the boundary). Symplectic cohomology for Liouville domains was introduced by Cieliebak–Floer–Hofer–Wysocki and Viterbo. The latter constructed a restriction (or transfer) map associated to an embedding of one Liouville domain into another. In this preprint, we look at exact Lagrangian submanifolds with Legendrian boundary inside a Liouville domain. The analogue of symplectic cohomology for such submanifolds is called “wrapped Floer cohomology”. We construct an –structure on the underlying wrapped Floer complex, and (under suitable assumptions) an –homomorphism realizing the restriction to a Liouville subdomain. The construction of the –structure relies on an implementation of homotopy direct limits, and involves some new moduli spaces which are solutions of generalized continuation map equations. |
Keywords
Lagrangian Floer homology
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Mathematical Subject Classification 2000
Primary: 53D40
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References |
Publication
Received: 8 January 2008
Revised: 15 August 2009
Accepted: 12 October 2009
Published: 16 February 2010
Proposed: Yasha Eliashberg
Seconded: Simon Donaldson, Leonid Polterovich
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Authors |
| Mohammed Abouzaid | |
| Department of Mathematics Massachusetts Institute of Technology 77 Massachusetts Ave Cambridge MA 02139 USA |
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| Paul Seidel | |
| Department of Mathematics Massachusetts Institute of Technology 77 Massachusetts Ave Cambridge MA 02139 USA |
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