Unexpected essential surfaces among exteriors of twisted torus knots

de Paiva, Thiago

doi:10.2140/agt.2022.22.3965

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Unexpected essential surfaces among exteriors of twisted torus knots

Thiago de Paiva

Algebraic & Geometric Topology 22 (2022) 3965–3982

DOI: 10.2140/agt.2022.22.3965

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.

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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

Volume 22, issue 8 (2022)