Algebraic & Geometric Topology

The periodic Floer homology of a Dehn twist

Michael Hutchings and Michael G Sullivan

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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 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
Received: 9 October 2004
Accepted: 8 March 2005
First available in Project Euclid: 20 December 2017

Permanent link to this document
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

Keywords
periodic Floer homology Dehn twist surface symplectomorphism

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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