Hyperbolic Knots given by Positive Braids with at Least two Full Twists

TL;DR

This paper establishes conditions under which positive braids with multiple full twists produce hyperbolic knots, aiding in the classification of T-links and twisted torus knots from a geometric perspective.

Contribution

It provides new criteria linking positive braid structures with hyperbolic knot properties, expanding understanding of knot classification.

Findings

Certain positive braids with two or more full twists yield hyperbolic knots.

Applications to classifying T-links and twisted torus knots.

Enhanced understanding of the geometric structure of these knots.

Abstract

We give some conditions on positive braids with at least two full twists that ensure their closure is a hyperbolic knot, with applications to the geometric classification of T-links, arising from dynamics, and twisted torus knots.