Bridge spheres for the unknot are topologically minimal

TL;DR

The paper proves that for the unknot, an (n+1)-bridge sphere is a topologically minimal surface with an index not exceeding n, providing insights into the topology of bridge spheres.

Contribution

It establishes a bound on the topological minimality index of bridge spheres for the unknot, linking bridge number to topological minimality.

Findings

(n+1)-bridge sphere for the unknot has index at most n

Bridge spheres are topologically minimal surfaces

Provides a new bound relating bridge number and minimality index

Abstract

We show that an $(n+1)$-bridge sphere for the unknot is a topologically minimal surface of index at most $n$.