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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Small knot complements, exceptional surgeries and hidden symmetries

Neil R Hoffman

Algebraic & Geometric Topology 14 (2014) 3227–3258
Abstract

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.

Keywords
knot complements, commensurability, hidden symmetries, exceptional surgeries, trace field
Mathematical Subject Classification 2010
Primary: 57M12, 57M25
Secondary: 57M10
References
Publication
Received: 15 December 2011
Revised: 9 December 2013
Accepted: 29 January 2014
Published: 15 January 2015
Authors
Neil R Hoffman
Department of Mathematics and Statistics
University of Melbourne
Parkville, Victoria 3010
Australia