Small knot complements, exceptional surgeries, and hidden symmetries

Neil Hoffman

doi:10.2140/agt.2014.14.3227

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arXiv · 1110.3863

Small knot complements, exceptional surgeries, and hidden symmetries

Neil Hoffman

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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.

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Neil Hoffman. 2011-10-18. Small knot complements, exceptional surgeries, and hidden symmetries. https://doi.org/10.2140/agt.2014.14.3227

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