An infinite family of links with critical bridge spheres

Abstract

A closed orientable splitting surface in an oriented 3–manifold is a topologically minimal surface of index $n$ if its associated disk complex is $\left(n-2\right)$–connected but not $\left(n-1\right)$–connected. A critical surface is a topologically minimal surface of index 2. In this paper, we use an equivalent combinatorial definition of critical surfaces to construct the first known critical bridge spheres for nontrivial links.