Legendrian knots, transverse knots and combinatorial Floer homology

Ozsváth, Peter; Szabó, Zoltán; Thurston, Dylan P

doi:10.2140/gt.2008.12.941

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Legendrian knots, transverse knots and combinatorial Floer homology

Peter Ozsváth, Zoltán Szabó and Dylan Thurston

Geometry & 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 2000

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 Thurston
Department of Mathematics, Barnard College Columbia University New York, NY 10027

Volume 12, issue 2 (2008)