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An infinite family of links with critical bridge spheres

Daniel Rodman

Algebraic & Geometric Topology 18 (2018) 153–186
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 (n2)–connected but not (n1)–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.

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Keywords
bridge sphere, link, topologically minimal, critical, plat position
Mathematical Subject Classification 2010
Primary: 57M25
References
Publication
Received: 17 February 2016
Revised: 6 May 2017
Accepted: 10 July 2017
Published: 10 January 2018
Authors
Daniel Rodman
Mathematics Department
Taylor University
Upland, IN
United States