#### Volume 14, issue 6 (2014)

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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 ${S}^{3}$ 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