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arXiv · 2501.02617

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

Julien Korinman
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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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Julien Korinman. 2025-01-05. Skein modules of closed 3 manifolds define line bundles over character varieties. https://arxiv.org/abs/2501.02617

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