A topological model for the HOMFLY-PT polynomial
Geometric Topology
2025-12-09 v2 Algebraic Topology
Abstract
We give the first known topological model for the HOMFLY-PT polynomial constructed directly from link diagrams. More precisely, we prove that this invariant is given by graded intersections between explicit Lagrangian submanifolds in a fixed configuration space on a Heegaard surface for the link exterior. The submanifolds are supported on a collection of arcs and ovals on the Heegaard surface. We also obtain two topological models for the Jones polynomial via a Heegaard surface associated to a link diagram. This opens up new avenues for constructing categorifications for the Jones and the HOMFLY-PT polynomials of a geometric nature.
Cite
@article{arxiv.2405.03679,
title = {A topological model for the HOMFLY-PT polynomial},
author = {Cristina Ana-Maria Anghel and Christine Ruey Shan Lee},
journal= {arXiv preprint arXiv:2405.03679},
year = {2025}
}
Comments
58 pages, comments welcome