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2017 A categorification of the Alexander polynomial in embedded contact homology
Gilberto Spano
Algebr. Geom. Topol. 17(4): 2081-2124 (2017). DOI: 10.2140/agt.2017.17.2081

Abstract

Given a transverse knot K in a three-dimensional contact manifold (Y,α), Colin, Ghiggini, Honda and Hutchings defined a hat version ECK̂(K,Y,α) of embedded contact homology for K and conjectured that it is isomorphic to the knot Floer homology HFK̂(K,Y ).

We define here a full version ECK(K,Y,α) and generalize the definitions to the case of links. We prove then that if Y = S3, then ECK and ECK̂ categorify the (multivariable) Alexander polynomial of knots and links, obtaining expressions analogous to that for knot and link Floer homologies in the minus and, respectively, hat versions.

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Gilberto Spano. "A categorification of the Alexander polynomial in embedded contact homology." Algebr. Geom. Topol. 17 (4) 2081 - 2124, 2017. https://doi.org/10.2140/agt.2017.17.2081

Information

Received: 9 February 2016; Revised: 5 December 2016; Accepted: 26 December 2016; Published: 2017
First available in Project Euclid: 16 November 2017

zbMATH: 1373.57033
MathSciNet: MR3685603
Digital Object Identifier: 10.2140/agt.2017.17.2081

Subjects:
Primary: 57M27 , 57R17 , 57R58

Keywords: Alexander polynomial , categorification , embedded contact homology

Rights: Copyright © 2017 Mathematical Sciences Publishers

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