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Link splitting deformation of colored Khovanov--Rozansky homology
Matthew Hogancamp, David E. V. Rose, Paul Wedrich
We introduce a multi-parameter deformation of the triply-graded Khovanov--Rozansky homology of links colored by one-column Young diagrams, generalizing the "-ified" link homolog…
A skein relation for singular Soergel bimodules
Matthew Hogancamp, David E. V. Rose, Paul Wedrich
We study the skein relation that governs the HOMFLYPT invariant of links colored by one-column Young diagrams. Our main result is a categorification of this colored skein relation.…
Tautological classes and symmetry in Khovanov-Rozansky homology
Eugene Gorsky, Matthew Hogancamp, Anton Mellit
We define a new family of commuting operators in Khovanov-Rozansky link homology, similar to the action of tautological classes in cohomology of character varieties. We prove…