The HOMFLY Polynomial of a Forest Quiver

Abstract

We define the HOMFLY polynomial of a forest quiver $Q$ 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 $Q$. We also prove a closed-form expression for the HOMFLY polynomial of a forest quiver $Q$ in terms of the independent sets of $Q$.

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