On weak reducing disks for the unknot in $3$-bridge position

TL;DR

This paper proves that the complex of weak reducing disks for the unknot in 3-bridge position is contractible, providing insight into the topological structure of such disks.

Contribution

It establishes the contractibility of the complex of weak reducing disks for the unknot in 3-bridge position, a new topological property.

Findings

The complex is contractible.

Implications for unknot and bridge position topology.

Advances understanding of disk complexes in knot theory.

Abstract

We show that the complex of weak reducing disks for the unknot in $3$-bridge position is contractible.