A categorification for the partial-dual genus polynomial
Fundamenta Mathematicae
MSC: Primary 57M15; Secondary 05C10
DOI: 10.4064/fm250612-21-2
Published online: 3 July 2026
Abstract
The partial-dual genus polynomial $^\partial \varepsilon _G(z)$ of a ribbon graph $G$ is the generating function that enumerates all partial duals of $G$. We exhibit a categorification for this polynomial. The key ingredient of the construction is an extended Frobenius algebra related to unoriented topological quantum field theory.
