Unknotting number for Lorenz knots

TL;DR

This paper investigates the unknotting number of Lorenz knots, a special class of positive braids, by deriving a new method to compute their unknotting numbers based on their Lorenz attractor positions.

Contribution

It introduces a novel approach to determine the unknotting number of Lorenz knots, extending the known results for positive braids.

Findings

Unknotting numbers for Lorenz knots are explicitly calculated.

The method relates Lorenz attractor positions to knot complexity.

Results provide a new perspective on knot invariants for Lorenz knots.

Abstract

The unknotting number of a positive braid with n strands and k intersections is known to be equal to (k-n+1)/2. We consider Lorenz knots (which are positive braids) and, using a different method, find their unknotting numbers in terms of their positions on the Lorenz attractor.