English

On keen weakly reducible bridge spheres

Geometric Topology 2023-03-28 v2

Abstract

A bridge sphere is said to be keen weakly reducible if it admits a unique pair of disjoint compressing disks on opposite sides. In particular, such a bridge sphere is weakly reducible, not perturbed, and not topologically minimal in the sense of David Bachman. In terms of Jennifer Schultens' width complex, a link in bridge position with respect to a keen weakly reducible bridge sphere is distance one away from a local minimum. In this paper, we give infinitely many examples of keen weakly reducible bridge spheres for links in bb bridge position for b4.b \geq 4.

Keywords

Cite

@article{arxiv.2009.11984,
  title  = {On keen weakly reducible bridge spheres},
  author = {Puttipong Pongtanapaisan and Daniel Rodman},
  journal= {arXiv preprint arXiv:2009.11984},
  year   = {2023}
}
R2 v1 2026-06-23T18:46:56.367Z