A categorification for the partial-dual genus polynomial

Zhiyun Cheng; Ziyi Lei

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arXiv · 2401.03632

A categorification for the partial-dual genus polynomial

Zhiyun Cheng·Ziyi Lei

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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 $G$. 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.

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Zhiyun Cheng, Ziyi Lei. 2024-01-08. A categorification for the partial-dual genus polynomial. https://arxiv.org/abs/2401.03632

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