The periodic Floer homology of a Dehn twist

Abstract

The periodic Floer homology of a surface symplectomorphism, defined by the first author and M. Thaddeus, is the homology of a chain complex which is generated by certain unions of periodic orbits, and whose differential counts certain embedded pseudoholomorphic curves in R cross the mapping torus. It is conjectured to recover the Seiberg-Witten Floer homology of the mapping torus for most spin-c structures, and is related to a variant of contact homology. In this paper we compute the periodic Floer homology of some Dehn twists.

Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol5/agt-5-14.abs.html

References in corpus (3)

• Rounding corners of polygons and the embedded contact homology of T^3
• Pseudoholomorphic punctured spheres in R x (S^1 x S^2) : Properties and existence
• Heegaard Floer homology of certain mapping tori

Cited by in corpus (20)

• HF=HM I : Heegaard Floer homology and Seiberg--Witten Floer homology
• Lagrangian matching invariants for fibred four-manifolds: II
• Rounding corners of polygons and the embedded contact homology of T^3
• Heegaard Floer homology and genus one, one boundary component open books
• Lagrangian matching invariants for fibred four-manifolds: I
• The equivalence of Heegaard Floer homology and embedded contact homology III: from hat to plus
• Symplectic Floer homology of area-preserving surface diffeomorphisms
• Vortices and a TQFT for Lefschetz fibrations on 4-manifolds
• Pseudoholomorphic punctured spheres in R x (S^1 x S^2) : Properties and existence
• Proof of the simplicity conjecture
• Khovanov homology and the cinquefoil
• Heegaard Floer homology of certain mapping tori
• Combinatorial embedded contact homology for toric contact manifolds
• PFH spectral invariants and $C^{\infty }$ closing lemmas
• Mirror symmetry for the Tate curve via tropical and log corals
• A categorification of the Alexander polynomial in embedded contact homology
• A Holomorphic 0-Surgery Model for Open Books with Application to Cylindrical Contact Homology
• Cobordism maps on periodic Floer homology induced by elementary Lefschetz fibrations
• Product and Coproduct on Fixed Point Floer Homology of Positive Dehn Twists
• Braids and linked periodic orbits of disc homeomorphisms