Algebraic and Geometric Topology 5 (2005), paper no. 14, pages 301-354.

The periodic Floer homology of a Dehn twist

Michael Hutchings, Michael Sullivan

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.

Keywords. Periodic Floer homology, Dehn twist, surface symplectomorphism

AMS subject classification. Primary: 57R58. Secondary: 53D40, 57R50.

DOI: 10.2140/agt.2005.5.301

E-print: arXiv:math.SG/0410059

Submitted: 9 October 2004. Accepted: 8 March 2005. Published: 17 April 2005.

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Michael Hutchings, Michael Sullivan
Department of Mathematics, University of California
Berkeley CA 94720-3840, USA
and
Department of Mathematics and Statistics, University of Massachusetts
Amherst, MA 01003-9305, USA
Email: hutching@math.berkeley.edu, sullivan@math.umass.edu

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