On keen weakly reducible bridge spheres

Puttipong Pongtanapaisan; Daniel Rodman

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arXiv · 2009.11984

On keen weakly reducible bridge spheres

Puttipong Pongtanapaisan·Daniel Rodman

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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 $b$ bridge position for $b \geq 4.$

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Puttipong Pongtanapaisan, Daniel Rodman. 2020-09-24. On keen weakly reducible bridge spheres. https://arxiv.org/abs/2009.11984

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