The flip symmetry on Khovanov-Rozansky homology
The flip symmetry on Khovanov-Rozansky homology
-
Hongjian Yang, Stanford University
Fine Hall 314
Inspired by the conjugation symmetry in involutive Heegaard Floer homology, we introduce and study the flip symmetry on Khovanov-Rozansky gl_N homology. This symmetry induces an involution on the gl_N homology, and we prove that it is in fact the identity. This allows us to prove that two involutions on the Khovanov homology of strongly invertible knots coincide. I’ll first explain the idea of the proof in the ordinary Khovanov homology setting and then describe how it generalizes to the gl_N case. This talk is based in part on joint work with Daren Chen.