Volume 13, issue 5 (2009)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 28
Issue 5, 1995–2482
Issue 4, 1501–1993
Issue 3, 1005–1499
Issue 2, 497–1003
Issue 1, 1–496

Volume 27, 9 issues

Volume 26, 8 issues

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Procedure
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN 1364-0380 (online)
ISSN 1465-3060 (print)
Author Index
To Appear
 
Other MSP Journals
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