The periodic Floer homology of a Dehn twist

Hutchings, Michael; Sullivan, Michael G

doi:10.2140/agt.2005.5.301

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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

DOI: 10.2140/agt.2005.5.301

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

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Publication

Received: 9 October 2004

Accepted: 8 March 2005

Published: 17 April 2005

Authors

Michael Hutchings
Department of Mathematics University of California Berkeley CA 94720-3840 USA

Michael G Sullivan
Department of Mathematics and Statistics University of Massachusetts Amherst MA 01003-9305 USA

Volume 5, issue 1 (2005)