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Abstract
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A closed orientable splitting surface in an oriented 3–manifold is a topologically minimal surface of index
if its associated disk
complex is
–connected
but not
–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
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Mathematical Subject Classification 2010
Primary: 57M25
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Publication
Received: 17 February 2016
Revised: 6 May 2017
Accepted: 10 July 2017
Published: 10 January 2018
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