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Unexpected essential surfaces among exteriors of twisted torus knots

Thiago de Paiva

Algebraic & Geometric Topology 22 (2022) 3965–3982
Abstract

The twisted torus knots T(p,q;r,s) are obtained by performing a sequence of s full twists on r adjacent strands of (p,q)–torus knots. Morimoto asked whether all twisted torus knots with essential tori in the exterior fit into one of two families. We prove that the answer to this question is no, by finding two different new families of toroidal twisted torus knots.

Keywords
twisted torus knots, satellite knots, Dehn surgery, essential surfaces
Mathematical Subject Classification
Primary: 57K10, 57K35
References
Publication
Received: 11 January 2021
Revised: 11 May 2021
Accepted: 5 September 2021
Published: 14 March 2023
Authors
Thiago de Paiva
School of Mathematics
Monash University
Melbourne
Australia