Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc.

Published online July 21, 2022

Copyright © The Korean Mathematical Society.

New families of hyperbolic twisted torus knots with generalized torsion

Keisuke Himeno and Masakazu Teragaito

Hiroshima University

Abstract

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 knot

MSC numbers: 57K10

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