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Legendrian knots, transverse knots and combinatorial Floer homology

Peter Ozsváth, Zoltán Szabó and Dylan P Thurston

Geometry and Topology 12 (2008) 941–980

DOI: 10.2140/gt.2008.12.941
Abstract

Using the combinatorial approach to knot Floer homology, we define an invariant for Legendrian knots (or links) in the three-sphere, with values in knot Floer homology. This invariant can also be used to construct an invariant of transverse knots.

Keywords

Legendrian knots, Floer homology
Mathematical Subject Classification

Primary: 53D12, 57R17, 57R58

Secondary: 57M25
References
Publication

Received: 21 February 2007
Revised: 5 January 2008
Accepted: 13 February 2008
Published: 12 May 2008
Proposed: Yasha Eliashberg
Seconded: Tom Mrowka, John Morgan
Authors
Peter Ozsváth
Department of Mathematics
Columbia University
New York, NY 10027
Zoltán Szabó
Department of Mathematics
Princeton University
Princeton, New Jersey 08544
Dylan P Thurston
Department of Mathematics, Barnard College
Columbia University
New York, NY 10027