Hidden symmetries via hidden extensions
Eric Chesebro, Jason DeBlois
TL;DR
This paper presents a novel method for identifying hidden symmetries in knots and links through the concept of hidden extensions, expanding understanding of symmetries in hyperbolic link complements.
Contribution
It introduces the concept of hidden extensions and demonstrates their application to reveal hidden symmetries in hyperbolic link complements.
Findings
Identification of a family of tangle complements with boundary symmetries
Extension of boundary symmetries to hidden symmetries of hyperbolic links
New insights into the structure of symmetries in knot and link complements
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.
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