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 $(n-2)$-connected but not $(n-1)$-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.

32 pages, 36 figures

References in corpus (2)

• Bridge distance and plat projections
• Bridge spheres for the unknot are topologically minimal