## Algebraic & Geometric Topology

### 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.

#### Article information

Source
Algebr. Geom. Topol., Volume 5, Number 1 (2005), 301-354.

Dates
Accepted: 8 March 2005
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.agt/1513796403

Digital Object Identifier
doi:10.2140/agt.2005.5.301

Mathematical Reviews number (MathSciNet)
MR2135555

Zentralblatt MATH identifier
1089.57021

Subjects
Primary: 57R58: Floer homology
Secondary: 53D40: Floer homology and cohomology, symplectic aspects 57R50: Diffeomorphisms

#### Citation

Hutchings, Michael; Sullivan, Michael G. The periodic Floer homology of a Dehn twist. Algebr. Geom. Topol. 5 (2005), no. 1, 301--354. doi:10.2140/agt.2005.5.301. https://projecteuclid.org/euclid.agt/1513796403

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