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

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.

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Item Permalink: http://hdl.handle.net/21.11116/0000-0007-A221-C Version Permalink: http://hdl.handle.net/21.11116/0000-0007-A222-B
Genre: Journal Article
Latex : Infinite families of hyperbolic $3$-manifolds with finite dimensional skein modules

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arXiv:1903.07686.pdf (Preprint), 569KB
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https://doi.org/10.1112/jlms.12410 (Publisher version)
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 Creators:
Detcherry, Renaud1, Author              
Affiliations:
1Max Planck Institute for Mathematics, Max Planck Society, ou_3029201              

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Free keywords: Mathematics, Geometric Topology
 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.

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Language(s): eng - English
 Dates: 2020
 Publication Status: Accepted / In Press
 Pages: -
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 Table of Contents: -
 Rev. Type: Peer
 Identifiers: arXiv: 1903.07686
DOI: 10.1112/jlms.12410
 Degree: -

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Title: Journal of the London Mathematical Society
  Abbreviation : J. Lond. Math. Soc.
Source Genre: Journal
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Publ. Info: Wiley
Pages: - Volume / Issue: - Sequence Number: Published Online - Print pending Start / End Page: - Identifier: -