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Abstract
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This paper provides two obstructions to small knot complements in
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.
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Keywords
knot complements, commensurability, hidden symmetries,
exceptional surgeries, trace field
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Mathematical Subject Classification 2010
Primary: 57M12, 57M25
Secondary: 57M10
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Publication
Received: 15 December 2011
Revised: 9 December 2013
Accepted: 29 January 2014
Published: 15 January 2015
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