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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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arXiv:1903.07686.pdf
(Preprint), 569KB

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Citation

Detcherry, R. (in press). Infinite families of hyperbolic 3-manifolds with finite dimensional skein modules. Journal of the London Mathematical Society, Published Online - Print pending. doi:10.1112/jlms.12410.


Cite as: http://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.