Volume 13, issue 5 (2009)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Symplectic Floer homology of area-preserving surface diffeomorphisms

Andrew Cotton-Clay

Geometry & Topology 13 (2009) 2619–2674
Abstract

The symplectic Floer homology HF(ϕ) of a symplectomorphism ϕ: Σ Σ encodes data about the fixed points of ϕ using counts of holomorphic cylinders in × Mϕ, where Mϕ is the mapping torus of ϕ. We give an algorithm to compute HF(ϕ) for ϕ a surface symplectomorphism in a pseudo-Anosov or reducible mapping class, completing the computation of Seidel’s HF(h) for h any orientation-preserving mapping class.

Keywords
Floer homology, symplectomorphism, surface diffeomorphism, mapping class group, fixed point, Nielsen class
Mathematical Subject Classification 2000
Primary: 53D40, 37J10
References
Publication
Received: 18 July 2008
Revised: 29 April 2009
Accepted: 5 February 2009
Published: 30 July 2009
Proposed: Peter Ozsváth
Seconded: Yasha Eliashberg, Leonid Polterovich
Authors
Andrew Cotton-Clay
Department of Mathematics
Harvard University
One Oxford St
Cambridge, MA 01238
USA
http://math.harvard.edu/~acotton