A categorification for the partial-dual genus polynomial

Zhiyun Cheng; Ziyi Lei

A categorification for the partial-dual genus polynomial

Geometric Topology 2024-01-09 v1 Combinatorics

Authors: Zhiyun Cheng , Ziyi Lei

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.

Keywords

graph polynomials

Cite

@article{arxiv.2401.03632,
  title  = {A categorification for the partial-dual genus polynomial},
  author = {Zhiyun Cheng and Ziyi Lei},
  journal= {arXiv preprint arXiv:2401.03632},
  year   = {2024}
}

Comments

31 pages, 13 figures

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