Knot commensurability and the Berge conjecture

Boileau, Michel; Boyer, Steven; Cebanu, Radu et Walsh, Genevieve S (2012). « Knot commensurability and the Berge conjecture ». Geometry & Topology, 16(2), pp. 625-664.

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Résumé

We investigate commensurability classes of hyperbolic knot complements in the generic case of knots without hidden symmetries. We show that such knot complements which are commensurable are cyclically commensurable, and that there are at most 3 hyperbolic knot complements in a cyclic commensurability class. Moreover if two hyperbolic knots have cyclically commensurable complements, then they are fibred with the same genus and are chiral. A characterization of cyclic commensurability classes of complements of periodic knots is also given. In the nonperiodic case, we reduce the characterization of cyclic commensurability classes to a generalization of the Berge conjecture.

Type:	Article de revue scientifique
Mots-clés ou Sujets:	Knot commensurability; Berge conjecture
Unité d'appartenance:	Faculté des sciences > Département de mathématiques
Déposé par:	Steven P. Boyer
Date de dépôt:	18 avr. 2016 17:20
Dernière modification:	27 avr. 2016 18:13
Adresse URL :	http://archipel.uqam.ca/id/eprint/8170

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