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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
A categorification of the Alexander polynomial in embedded contact homology

Gilberto Spano

Algebraic & Geometric Topology 17 (2017) 2081–2124
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.

Keywords
embedded contact homology, Alexander polynomial, categorification
Mathematical Subject Classification 2010
Primary: 57M27, 57R17, 57R58
References
Publication
Received: 9 February 2016
Revised: 5 December 2016
Accepted: 26 December 2016
Published: 3 August 2017
Authors
Gilberto Spano
Institut Fourier
Université Grenoble Alpes
38000 Grenoble
France