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

Detcherry, Renaud

doi:10.1112/jlms.12410

Item

ITEM ACTIONSEXPORT

Add to Basket

Local TagsStatisticsRelease HistoryDetailsSummary

Released

Journal Article

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

MPS-Authors

/persons/resource/persons249038

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

External Ressource

https://doi.org/10.1112/jlms.12410
(Publisher version)

Fulltext (public)

arXiv:1903.07686.pdf
(Preprint), 569KB

Supplementary Material (public)

There is no public supplementary material available

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.