English

The HOMFLY Polynomial of a Forest Quiver

Combinatorics 2026-04-20 v2 Geometric Topology

Abstract

We define the HOMFLY polynomial of a forest quiver QQ using a recursive definition on the underlying graph of the quiver. We then show that this polynomial is equal to the HOMFLY polynomial of any plabic link which comes from a connected plabic graph whose quiver is QQ. We also prove a closed-form expression for the HOMFLY polynomial of a forest quiver QQ in terms of the independent sets of QQ.

Keywords

Cite

@article{arxiv.2410.00399,
  title  = {The HOMFLY Polynomial of a Forest Quiver},
  author = {Amanda Schwartz},
  journal= {arXiv preprint arXiv:2410.00399},
  year   = {2026}
}

Comments

29 pages, 25 figures; Version 2 contains a closed formula for the HOMFLY polynomial which generalizes the formula for the Alexander polynomial from version 1