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Knot commensurability and
the Berge conjecture
Michel Boileau, Steven Boyer, Radu Cebanu and Genevieve S Walsh |
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Geometry & Topology 16 (2012) 625–664
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Abstract |
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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 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. |
Keywords
hyperbolic knot, commensurability
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Mathematical Subject Classification 2010
Primary: 57M10, 57M25
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References |
Publication
Received: 8 February 2011
Accepted: 27 November 2011
Published: 18 April 2012
Proposed: Cameron Gordon
Seconded: Walter Neumann, Colin Rourke
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Authors |
| Michel Boileau | |
| Institut de Mathématiques de
Toulouse Université Paul Sabatier 118 route de Narbonne F-31062 Toulouse Cedex 9 France |
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| http://picard.ups-tlse.fr/homepage/boileau.html | |
| Steven Boyer | |
| Département de mathématiques Université du Québec à Montréal PO Box 8888 Centre-ville Montréal QC H3C 3P8 Canada |
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| http://www.cirget.uqam.ca/boyer/boyer.html | |
| Radu Cebanu | |
| Département de mathématiques Université du Québec à Montréal PO Box 8888 Centre-ville Montréal QC H3C 3P8 Canada |
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| Genevieve S Walsh | |
| Department of Mathematics Tufts University 503 Boston Ave Medford MA 02155 USA |
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| http://www.tufts.edu/~gwalsh01/ | |
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