The HOMFLY Polynomial of a Forest Quiver
Combinatorics
2026-04-20 v2 Geometric Topology
Abstract
We define the HOMFLY polynomial of a forest quiver 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 . We also prove a closed-form expression for the HOMFLY polynomial of a forest quiver in terms of the independent sets of .
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