Non-determinacy of HOMFLY-PT homology for diagrams

Maciej Borodzik, Mikhail Malashchuk

We show that for any two knots $K_1$, $K_2$ in ${\mathbb{R}}^3$, there exist diagrams $D_1$ and $D_2$ that represent $K_1$ and $K_2$, respectively, such that the Khovanov--Rozansky t…