Small knot complements, exceptional surgeries and hidden symmetries

Hoffman, Neil R¹

¹Department of Mathematics and Statistics, University of Melbourne, Parkville, Victoria 3010, Australia

Algebraic and Geometric Topology, Tome 14 (2014) no. 6, pp. 3227-3258

Résumé

This paper provides two obstructions to small knot complements in S3 admitting hidden symmetries. The first obstruction is being cyclically commensurable with another knot complement. This result provides a partial answer to a conjecture of Boileau, Boyer, Cebanu and Walsh. We also provide a second obstruction to admitting hidden symmetries in the case where a small knot complement covers a manifold admitting some symmetry and at least two exceptional surgeries.

Détail

DOI : 10.2140/agt.2014.14.3227

Classification : 57M12, 57M25, 57M10
Keywords: knot complements, commensurability, hidden symmetries, exceptional surgeries, trace field

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