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G&T Monographs |
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Symplectic Floer homology of area-preserving surface
diffeomorphisms
Andrew Cotton-Clay
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Geometry & Topology 13 (2009)
2619–2674
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Abstract
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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 R × 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.
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Keywords
Floer homology, symplectomorphism,
surface diffeomorphism, mapping class group, fixed point,
Nielsen class
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Mathematical Subject Classification
Primary: 37J10, 53D40
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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
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