Skein modules of closed 3 manifolds define line bundles over character varieties
Quantum Algebra
2025-01-07 v1 Geometric Topology
Abstract
Let M be a closed 3-manifold and S(M) the skein module of M at some odd root of unity. Using the Frobenius morphism, we can see S(M) as the space of global sections of a coherent sheaf over the SL2 character scheme of M. We prove that when the character scheme is reduced, this sheaf is a line bundle.
Cite
@article{arxiv.2501.02617,
title = {Skein modules of closed 3 manifolds define line bundles over character varieties},
author = {Julien Korinman},
journal= {arXiv preprint arXiv:2501.02617},
year = {2025}
}