An open string analogue of Viterbo functoriality

2007/12/31 by Mohammed Abouzaid, Paul Seidel · 157 citations
Mathematics · #Boundary (topology) #Cohomology #Domain (mathematical analysis) #Embedding #Geometric and Algebraic Topology #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #String (physics) #Symplectic geometry #Type (biology) #math.SG #msc:53D40

paper · pdf · doi:10.2140/gt.2010.14.627

published in Geometry & Topology 14(2), 627-718 (Mathematical Sciences Publishers) · 71 pages, 9 figures, minor revision correcting typographical errors and clarifying the exposition following a referee's comments

arxiv created 2009/08/25 · openalex publication_date 2010/02/16 · arxiv updated 2014/11/11 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

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.

Citations

• Exact Lagrangian submanifolds in simply-connected cotangent bundles
• Symplectic fixed points and holomorphic spheres

Cited by

• Fixed Point Floer Cohomology of Dehn Twists I: Splitting Formulas
• A Deformation of the Compact Fukaya Category via the Relative Fukaya Category
• Splitting symplectic monodromy

Related

• On weakly exact Lagrangians in Liouville bi-fillings
• An L_∞ structure on symplectic cohomology
• On the wrapped Fukaya category and the loop space of Lagrangians in a Liouville manifold
• The Constrained Symplectic Area Functional and its Floer Homology
• Functors of wrapped Fukaya categories from Lagrangian correspondences