A categorification of the Alexander polynomial in embedded contact homology

Spano, Gilberto¹

¹Institut Fourier, Université Grenoble Alpes, 38000 Grenoble, France

Algebraic and Geometric Topology, Tome 17 (2017) no. 4, pp. 2081-2124

Résumé

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.

Détail

DOI : 10.2140/agt.2017.17.2081

Classification : 57M27, 57R17, 57R58
Keywords: embedded contact homology, Alexander polynomial, categorification

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