The beauty of the HOMFLYPT polynomial is that it generalizes all sl(N) link
polynomials as well as the Alexander-Conway polynomial. In the categorified
setting the analogous relation has been found by Rasmussen in the form of a spectral
sequence from the categorified HOMFLYPT to sl(N) link homology for all N>0.
However, a similar relation to the categorified Alexander-Conway polynomial,
the Heegaard-Floer knot homology, is currently unknown, although the results
of Manolescu and Dowlin suggests that such a spectral sequence should exist.
In my talk I will show how to construct a spectral sequence (over a field of
characteristic other than 2) from the reduced HOMFLYPT homology to a certain
homology of a knot diagram that coincides with HFK over Z/2.
This is joint work with Anna Beliakova, Louis-Hadrien Robert and Emmanuel Wagner.
This talk was part of the conference "Perspectives on quantum link homology theories", see https://cbz20.raspberryip.com/Perspectives-2021