An open string analogue of Viterbo functoriality
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Author(s)
Abouzaid, Mohammed
Seidel, Paul
Date Issued
February 2010
Journal
Geometry and Topology
Publisher
Mathematical Sciences Publishers
Citation
Abouzaid, Mohammed, and Paul Seidel. “An Open String Analogue of Viterbo Functoriality.” Geometry & Topology 14.2 (2010): 627–718. Web.
Version
Author's final manuscript
Abstract
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
A[infinity symbol]–structure on the underlying wrapped Floer complex, and (under suitable assumptions) an A[infinity symbol]–homomorphism realizing the restriction to a Liouville subdomain. The construction of the A[infinity symbol]–structure relies on an implementation of homotopy direct limits, and involves some new moduli spaces which are solutions of generalized continuation map equations.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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DOI of Published Version
https://doi.org/10.2140/gt.2010.14.627
