Khovanov-Rozansky ${\mathfrak{sl}}_N$-homology for periodic links

Abstract

For an $m$-periodic link $L$, we show that the Khovanov-Rozansky ${\mathfrak{sl}}_N$-homology carries an action of the group ${\mathbb{Z}}_m$. As an example of applications, we prove an analog of the periodicity criterion of Borodzik--Politarczyk using ${\mathfrak{sl}}_N$-homology instead of Khovanov homology.

42 pages, 10 figures. v2: improved presentation. Comments are welcome!