Small knot complements, exceptional surgeries, and hidden symmetries

Details Small knot complements, exceptional surgeries, and hidden symmetries Small knot complements, exceptional surgeries, and hidden symmetries

2011-10-18

arxiv.org/abs/1110.3863v2

Mathematics

Geometric Topology

31 pages, 11 figures, v2 has updated references, minor edits for clarity, and corrections of a few typographical errors

Scientific paper

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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