Bridge spheres for the unknot are topologically minimal

Jung Hoon Lee

Vol. 282 (2016), No. 2, 437–443

DOI: 10.2140/pjm.2016.282.437

Abstract

Topologically minimal surfaces were defined by Bachman as topological analogues of geometrically minimal surfaces, and one can associate a topological index to each topologically minimal surface. We show that an $\left(n+1\right)$-bridge sphere for the unknot is a topologically minimal surface of index at most $n$.

Keywords

disk complex, topologically minimal surface, bridge splitting, unknot

Mathematical Subject Classification 2010

Primary: 57M50

Milestones

Received: 22 December 2014

Revised: 29 May 2015

Accepted: 2 July 2015

Published: 3 March 2016