Volume 11, issue 4 (2007)

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On combinatorial link Floer homology

Ciprian Manolescu, Peter Ozsváth, Zoltán Szabó and Dylan Thurston

Geometry & Topology 11 (2007) 2339–2412

arXiv: math.GT/0610559

Abstract

Link Floer homology is an invariant for links defined using a suitable version of Lagrangian Floer homology. In an earlier paper, this invariant was given a combinatorial description with mod 2 coefficients. In the present paper, we give a self-contained presentation of the basic properties of link Floer homology, including an elementary proof of its invariance. We also fix signs for the differentials, so that the theory is defined with integer coefficients.

Keywords
Floer homology
Mathematical Subject Classification 2000
Primary: 57R58, 57M25
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Publication
Received: 2 November 2006
Accepted: 12 June 2007
Published: 17 December 2007
Proposed: Rob Kirby
Seconded: Yasha Eliashberg, Tom Mrowka
Authors
Ciprian Manolescu
Department of Mathematics
Columbia University
New York NY 10027
USA
Peter Ozsváth
Department of Mathematics
Columbia University
New York NY 10027
USA
Zoltán Szabó
Department of Mathematics
Princeton University
Princeton NJ 08544
USA
Dylan Thurston
Department of Mathematics
Barnard College
Columbia University
New York NY 10027
USA