On Hecke lifting conjecture for framed knots
Geometric Topology
2025-10-20 v1 High Energy Physics - Theory
Abstract
Motivated by an amazing integrality structure conjecture for the Chern-Simons quantum invariants of framed knots investigated by Mari\~no and Vafa, a new conjectural formula, named Hecke lifting conjecture, was proposed in \cite{CLPZ23} for framed links. This note is devoted to the study of this Hecke lifting conjecture. We prove this conjecture for torus knots using the explicit formulas of colored HOMFLY-PT invariants of torus knots, and we also verify the conjecture in a limit form for any framed knots.
Cite
@article{arxiv.2510.15692,
title = {On Hecke lifting conjecture for framed knots},
author = {Shengmao Zhu},
journal= {arXiv preprint arXiv:2510.15692},
year = {2025}
}
Comments
17 pages