Symplectic Floer homology of area-preserving surface diffeomorphisms

2008/07/31 by Andrew Cotton-Clay · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #Algorithm #Class (philosophy) #Combinatorics #Computation #Computer science #Floer homology #Geometric and Algebraic Topology #Geometry #Holomorphic function #Homology (biology) #Mapping class group #Mathematical Dynamics and Fractals #Mathematical analysis #Mathematics #Pure mathematics #Surface (topology) #Symplectic geometry #Symplectomorphism #Torus #math.GT #math.SG #msc:37J10 #msc:53D40

paper · pdf · doi:10.2140/gt.2009.13.2619

published as Geom. Topol. 13 (2009) 2619-2674 · 57 pages, 4 figures. Revision for publication, with various minor corrections. Adds results on the module structure and invariance thereof

openalex publication_date 2009/07/30 · arxiv created 2010/09/03 · arxiv updated 2014/11/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

The symplectic Floer homology HF . / of a symplectomorphism W ! encodes data about the fixed points of using counts of holomorphic cylinders in R M , where M is the mapping torus of . We give an algorithm to compute HF . / for a surface symplectomorphism in a pseudo-Anosov or reducible mapping class, completing the computation of Seidel's HF .h/ for h any orientationpreserving mapping class.

Citations

• Morse theory for Lagrangian intersections
• On the geometry and dynamics of diffeomorphisms of surfaces
• Lagrangian matching invariants for fibred four-manifolds: II
• The Seiberg–Witten equations and the Weinstein conjecture
• Embedded contact homology and Seiberg–Witten Floer cohomology I
• Holomorphic disks and topological invariants for closed three-manifolds
• Self-Dual Instantons and Holomorphic Curves
• Train-tracks for surface homeomorphisms
• Symplectic fixed points and holomorphic spheres
• Introduction to Symplectic Field Theory
• Morse theory for periodic solutions of hamiltonian systems and the maslov index
• Rounding corners of polygons and the embedded contact homology ofT3
• The embedded contact homology index revisited
• Reeb vector fields and open book decompositions

Cited by

• Fixed Point Floer Cohomology of Dehn Twists I: Splitting Formulas

Related

• Floer Homology for Symplectomorphism
• Symplectic Floer homology and the mapping class group
• Floer homology of algebraically finite mapping classes
• Nielsen theory, Floer homology and a generalisation of the Poincare-Birkhoff theorem
• Periodic Floer homology and the smooth closing lemma for area-preserving surface diffeomorphisms