Skein modules of closed 3 manifolds define line bundles over character varieties

2025/01/05 by Julien Korinman, Korinman, Julien · 1 citation
Mathematics · #Homotopy and Cohomology in Algebraic Topology #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications

paper · pdf · doi:10.48550/arxiv.2501.02617

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.

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