Geometry & Topology

Legendrian knots, transverse knots and combinatorial Floer homology

Peter Ozsváth, Zoltán Szabó, and Dylan P Thurston

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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.

Article information

Source
Geom. Topol., Volume 12, Number 2 (2008), 941-980.

Dates
Received: 21 February 2007
Revised: 5 January 2008
Accepted: 13 February 2008
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.gt/1513800065

Digital Object Identifier
doi:10.2140/gt.2008.12.941

Mathematical Reviews number (MathSciNet)
MR2403802

Zentralblatt MATH identifier
1144.57012

Subjects
Primary: 53D12: Lagrangian submanifolds; Maslov index 57R17: Symplectic and contact topology 57R58: Floer homology
Secondary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45}

Keywords
Legendrian knots Floer homology

Citation

Ozsváth, Peter; Szabó, Zoltán; Thurston, Dylan P. Legendrian knots, transverse knots and combinatorial Floer homology. Geom. Topol. 12 (2008), no. 2, 941--980. doi:10.2140/gt.2008.12.941. https://projecteuclid.org/euclid.gt/1513800065


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