On discrete symmetries of the cube of smoothings

We study the Khovanov complex of closed piecewise linear curves in the 3-space. A polygonal link representation endows the cube of resolutions with an additional combinatorial structure. The set of symmetries preserving this structure and its quotient under link equivalence are studied. Our results offer new combinatorial ways of computing Khovanov homology and might lead to other group-theoretic invariants of links.