Given a transverse knot in a three-dimensional contact manifold , Colin, Ghiggini, Honda and Hutchings defined a hat version of embedded contact homology for and conjectured that it is isomorphic to the knot Floer homology .
We define here a full version and generalize the definitions to the case of links. We prove then that if , then and 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.
"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