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.
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