On keen weakly reducible bridge spheres

Pongtanapaisan, Puttipong; Rodman, Daniel

doi:10.2140/agt.2024.24.4201

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On keen weakly reducible bridge spheres

Puttipong Pongtanapaisan and Daniel Rodman

Algebraic & Geometric Topology 24 (2024) 4201–4235

DOI: 10.2140/agt.2024.24.4201

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. We give infinitely many examples of keen weakly reducible bridge spheres for links in $b$ bridge position for $b \geq 4$ .

Keywords

Bachman's topological index, curve complex, bridge positions

Mathematical Subject Classification

Primary: 57K10, 57K20, 57K30

References

Publication

Received: 24 September 2020

Revised: 6 April 2023

Accepted: 28 June 2023

Published: 17 December 2024

Authors

Puttipong Pongtanapaisan
Arizona State University Tempe, AZ United States

Daniel Rodman
Mathematics Department Taylor University Upland, IN United States

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Volume 24, issue 8 (2024)