A categorification for the partial-dual genus polynomial

Abstract

The partial-dual genus polynomial ${}^{\partial }{\epsilon }_G(z)$ of a ribbon graph $G$ is the generating function that enumerates all partial duals of $G$. In this paper, we give a categorification for this polynomial. The key ingredient of the construction is an extended Frobenius algebra related to unoriented topological quantum field theory.

31 pages, 13 figures