Infinite families of hyperbolic 3-manifolds with finite-dimensional skein 
modules

Detcherry, Renaud

doi:10.1112/jlms.12410

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Infinite families of hyperbolic 3-manifolds with finite-dimensional skein modules

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Detcherry, Renaud
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1112/jlms.12410
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https://doi.org/10.48550/arXiv.1903.07686
(Preprint)

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Citation

Detcherry, R. (2021). Infinite families of hyperbolic 3-manifolds with finite-dimensional skein modules. Journal of the London Mathematical Society, 103(4), 1363-1376. doi:10.1112/jlms.12410.

Cite as: https://hdl.handle.net/21.11116/0000-0007-A221-C

Abstract

The Kauffman bracket skein module $K(M)$ of a $3$-manifold $M$ is the quotient of the $\mathbb{Q}(A)$-vector space spanned by isotopy classes of links in $M$ by the Kauffman relations. A conjecture of Witten states that if
$M$ is closed then $K(M)$ is finite dimensional. We introduce a version of this conjecture for manifolds with boundary and prove a stability property for generic Dehn-filling of knots. As a result we provide the first hyperbolic
examples of the conjecture, proving that almost all Dehn-fillings of any two-bridge knot satisfies the conjecture.