Volume 5, issue 1 (2005)

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The periodic Floer homology of a Dehn twist

Michael Hutchings and Michael G Sullivan

Algebraic & Geometric Topology 5 (2005) 301–354

arXiv: math.SG/0410059


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 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.

periodic Floer homology, Dehn twist, surface symplectomorphism
Mathematical Subject Classification 2000
Primary: 57R58
Secondary: 53D40, 57R50
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Received: 9 October 2004
Accepted: 8 March 2005
Published: 17 April 2005
Michael Hutchings
Department of Mathematics
University of California
Berkeley CA 94720-3840
Michael G Sullivan
Department of Mathematics and Statistics
University of Massachusetts
Amherst MA 01003-9305