Symplectic Floer homology of area-preserving surface diffeomorphisms

Cotton-Clay, Andrew¹

¹ Department of Mathematics, Harvard University, One Oxford St, Cambridge, MA 01238, USA

Geometry & topology, Tome 13 (2009) no. 5, pp. 2619-2674.

Résumé

The symplectic Floer homology ${HF}_{\ast }\left(\varphi \right)$ of a symplectomorphism $\varphi :\Sigma \to \Sigma$ encodes data about the fixed points of $\varphi$ using counts of holomorphic cylinders in $ℝ\times M_{\varphi }$, where $M_{\varphi }$ is the mapping torus of $\varphi$. We give an algorithm to compute ${HF}_{\ast }\left(\varphi \right)$ for $\varphi$ a surface symplectomorphism in a pseudo-Anosov or reducible mapping class, completing the computation of Seidel’s ${HF}_{\ast }\left(h\right)$ for $h$ any orientation-preserving mapping class.

Détail

DOI : 10.2140/gt.2009.13.2619

Keywords: Floer homology, symplectomorphism, surface diffeomorphism, mapping class group, fixed point, Nielsen class

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