Small knot complements, exceptional surgeries, and hidden symmetries

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.

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

References in corpus (3)

• Commensurability classes of 2-bridge knot complements
• Knot commensurability and the Berge conjecture
• Commensurability classes containing three knot complements

Cited by in corpus (1)

• Symmetries and hidden symmetries of $(\epsilon ,d_L)$-twisted knot complements