#### 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
##### 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
##### Mathematical Subject Classification 2000
Primary: 57R58
Secondary: 53D40, 57R50