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Bull. Korean Math. Soc. 2023; 60(1): 203-223

Online first article July 21, 2022      Printed January 31, 2023

https://doi.org/10.4134/BKMS.b220055

Copyright © The Korean Mathematical Society.

New families of hyperbolic twisted torus knots with generalized torsion

Keisuke Himeno, Masakazu Teragaito

1-3-1 Kagamiyama; 1-1-1 Kagamiyama

Abstract

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A generalized torsion element is an obstruction for a group to admit a bi-ordering. Only a few classes of hyperbolic knots are known to admit such an element in their knot groups. Among twisted torus knots, the known ones have their extra twists on two adjacent strands of torus knots. In this paper, we give several new families of hyperbolic twisted torus knots whose knot groups have generalized torsion. They have extra twists on arbitrarily large numbers of adjacent strands of torus knots.

Keywords: Twisted torus knots, generalized torsion

MSC numbers: Primary 57K10; Secondary 57M05, 06F15, 20F05, 20F60

Supported by: The second author has been partially supported by JSPS KAKENHI Grant Number JP20K03587.

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