Uniqueness of higher genus bridge surfaces for torus knots

TL;DR

This paper proves that non-2-bridge torus knots have a unique irreducible bridge splitting of positive genus, highlighting a distinctive topological property of these knots.

Contribution

It establishes the uniqueness of higher genus bridge surfaces for torus knots that are not 2-bridge, a novel result in knot theory.

Findings

Non-2-bridge torus knots have a unique irreducible bridge splitting of positive genus.

The result distinguishes these knots from 2-bridge torus knots in terms of bridge surface properties.

The proof advances understanding of the topology of torus knots and their decompositions.

Abstract

We show that a torus knot which is not 2-bridge has a unique irreducible bridge splitting of positive genus.