Hidden symmetries via hidden extensions

Abstract

This paper introduces a new approach to finding knots and links with hidden symmetries using "hidden extensions", a class of hidden symmetries defined here. We exhibit a family of tangle complements in the ball whose boundaries have symmetries with hidden extensions, then we further extend these to hidden symmetries of some hyperbolic link complements.

16 pages, 4 figures. Many changes suggested by a referee, including overhauled exposition in Section 1