Bridge surfaces with the topological minimality preserved by perturbation

2015/12/07 by Jung Hoon Lee, Lee, Jung Hoon
Mathematics · #57M99 #FOS: Mathematics #Geometric Topology (math.GT) #math.GT #msc:57M99

paper · pdf · doi:10.48550/arxiv.1512.01908

8 pages, 7 figures

arxiv created 2015/12/07 · arxiv updated 2015/12/08

Abstract

We show that except for n = 2 if a bridge surface for a knot is an index n topologically minimal surface, then after a perturbation it is still topologically minimal with index at most n+1.

Related

• On the existence of high index topologically minimal surfaces
• Uniqueness of bridge surfaces for 2-bridge knots
• Multiple bridge surfaces restrict knot distance
• Unperturbed weakly reducible non-minimal bridge positions
• Distance and bridge position