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Sutured Floer homology
and invariants of Legendrian and transverse knots
John B Etnyre, David Shea Vela-Vick and Rumen Zarev |
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Geometry & Topology 21 (2017) 1469–1582
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Abstract |
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Using contact-geometric techniques and sutured Floer homology, we present an alternate formulation of the minus and plus versions of knot Floer homology. We further show how natural constructions in the realm of contact geometry give rise to much of the formal structure relating the various versions of Heegaard Floer homology. In addition, to a Legendrian or transverse knot we associate distinguished classes and , which are each invariant under Legendrian or transverse isotopies of . The distinguished class is shown to agree with the Legendrian/transverse invariant defined by Lisca, Ozsváth, Stipsicz and Szabó despite a strikingly dissimilar definition. While our definitions and constructions only involve sutured Floer homology and contact geometry, the identification of our invariants with known invariants uses bordered sutured Floer homology to make explicit computations of maps between sutured Floer homology groups. |
Keywords
Legendrian knots, transverse knots, Heegaard Floer homology
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Mathematical Subject Classification 2010
Primary: 57M27
Secondary: 57R58, 57R17
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References |
Publication
Received: 4 September 2014
Revised: 25 April 2016
Accepted: 17 August 2016
Published: 10 May 2017
Proposed: Yasha Eliashberg
Seconded: András I. Stipsicz, Peter S. Ozsváth
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Authors |
| John B Etnyre | |
| School of Mathematics Georgia Institute of Technology 686 Cherry Street Atlanta, GA 30332-0160 United States |
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| http://people.math.gatech.edu/~etnyre/ | |
| David Shea Vela-Vick | |
| Department of Mathematics Louisiana State University Baton Rouge, LA 70803 United States |
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| https://www.math.lsu.edu/\~{}shea | |
| Rumen Zarev | |
| Department of Mathematics University of California, Berkeley 970 Evans Hall Berkeley, CA 94720-3840 United States |
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