Torus knots obtained by negatively twisting torus knots

TL;DR

This paper introduces eight new infinite families of twisted torus knots that are actually torus knots, achieved by adding a single negative twist along certain strands, expanding understanding of their structure.

Contribution

The paper provides new infinite families of twisted torus knots that are equivalent to torus knots through negative twisting, enhancing classification methods.

Findings

Identified eight new infinite families of such knots.

Demonstrated these knots are equivalent to torus knots via negative twists.

Expanded the catalog of known twisted torus knots with specific properties.

Abstract

Twisted torus knots are torus knots with some full twists added along some number of adjacent strands. There are infinitely many known examples of twisted torus knots which are actually torus knots. We give eight more infinite families of such twisted torus knots with a single negative twist.