Knot invariants arising from homological operations on Khovanov homology

There are several homological operations that can be defined between even and odd Khovanov homology theories using the unified homology theory developed by Putyra. This construction works for both reduced and unreduced versions of the Khovanov homology. We discuss these homological operations, compare different versions of them, and show how they can give rise to new knot invariants with interesting properties.
The talk is based on a joint work with Krzysztof Putyra [1]. The author is partially supported by a Simons Collaboration Grant for Mathematicians #279867.
References:

• K. Putyra and A. Shumakovitch, Knot invariants arising from homological operations on Khovanov homology. J. Knot Th. and Ramif. 25 (2016), no. 3, 1640012 [18 pages]; arXiv:1601.00798.