Constructions of q-hyperbolic knots
[Construction de noeuds q-hyperboliques]
Kalfagianni, Efstratia1 ; Melby, Joseph M.1
1 Department of Mathematics, Michigan State University, East Lansing, MI, 48824, USA
Annales de l'Institut Fourier, Online first, 29 p.

We use Dehn surgery methods to construct infinite families of hyperbolic knots in the 3-sphere satisfying a weak form of the Turaev–Viro invariants volume conjecture. The results have applications to a conjecture of Andersen, Masbaum and Ueno about quantum representations of surface mapping class groups. We obtain an explicit family of pseudo-Anosov mapping classes acting on surfaces of any genus and with one boundary component that satisfy the conjecture.

Nous utilisons des méthodes de chirurgie de Dehn pour construire des familles infinies de noeuds hyperboliques dans S 3 vérifiant une forme faible de la conjecture du volume pour les invariants de Turaev–Viro. Ces résultats ont des applications à la conjecture d’Andersen–Masbaum–Ueno sur les représentations quantiques des groupes de difféotopie des surfaces. Nous obtenons une famille explicite de difféotopies pour les surfaces de chaque genre à une composante de bord qui vérifient la conjecture

Reçu le :
Accepté le :
Première publication :
DOI : 10.5802/aif.3719
Classification : 57K31, 57M50, 57K16
Keywords: annulus presentation, Dehn surgery, double twist knot, hyperbolic knot, pseudo-Anosov mapping class, $q$-hyperbolic knot, quantum representation, Turaev–Viro invariants
Mots-clés : présentation en anneau, chirurgie de Dehn, noeud double twist, noeuds hyperboliques, difféotopie pseudo-Anosov, noeud q-hyperbolique, représentation quantique, invariants de Turaev–Viro

Kalfagianni, Efstratia 1 ; Melby, Joseph M. 1

1 Department of Mathematics, Michigan State University, East Lansing, MI, 48824, USA 
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Kalfagianni, Efstratia; Melby, Joseph M. Constructions of $q$-hyperbolic knots. Annales de l'Institut Fourier, Online first, 29 p.

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