Symplectic Floer homology of area-preserving surface diffeomorphisms

Abstract

The symplectic Floer homology HF_*(f) of a symplectomorphism f:S->S encodes data about the fixed points of f using counts of holomorphic cylinders in R x M_f, where M_f is the mapping torus of f. We give an algorithm to compute HF_*(f) for f a surface symplectomorphism in a pseudo-Anosov or reducible mapping class, completing the computation of Seidel's HF_*(h) for h any orientation-preserving mapping class.

57 pages, 4 figures. Revision for publication, with various minor corrections. Adds results on the module structure and invariance thereof

References in corpus (5)

• The Seiberg-Witten equations and the Weinstein conjecture
• Lagrangian matching invariants for fibred four-manifolds: II
• Vortices and a TQFT for Lefschetz fibrations on 4-manifolds
• Reeb vector fields and open book decompositions
• Floer Homology, Nielsen Theory and Symplectic Zeta Functions

Cited by in corpus (18)

• A symplectic proof of a theorem of Franks
• Contact Homology of Orbit Complements and Implied Existence
• Khovanov homology and the cinquefoil
• Small Dehn surgery and SU(2)
• Invariance property of Morse homology on noncompact manifolds
• Categorical lifting of the Jones polynomial: a survey
• PFH spectral invariants and $C^{\infty }$ closing lemmas
• A spectral sequence of the Floer cohomology of symplectomorphisms of trivial polarization class
• The cylindrical contact homology of universally tight sutured contact solid tori
• The embedded contact homology of sutured solid tori
• Fixed-point-free pseudo-Anosov homeomorphisms, knot Floer homology and the cinquefoil
• Floer cohomology and pencils of quadrics
• A categorification of the Alexander polynomial in embedded contact homology
• The growth rate of Floer homology and symplectic zeta function
• Product and Coproduct on Fixed Point Floer Homology of Positive Dehn Twists
• Braids and linked periodic orbits of disc homeomorphisms
• Floer homology and right-veering monodromy
• Mapping classes are almost determined by their finite quotient actions