Bridge spectra of iterated torus knots

2013/01/31 by Alexander Zupan, Zupan, Alexander
Mathematics · #57M25 #57M27 #FOS: Mathematics #Geometric Topology (math.GT) #math.GT #msc:57M25 #msc:57M27

paper · pdf · doi:10.48550/arxiv.1301.7689

32 pages, 6 figures

arxiv created 2013/01/31 · arxiv updated 2013/02/01

Abstract

We determine the set of all genus g bridge numbers of many iterated torus knots, listing these numbers in a sequence called the bridge spectrum. In addition, we prove a structural lemma about the decomposition of a strongly irreducible bridge surface induced by cutting along a collection of essential surfaces.

Related

• Bridge spectra of twisted torus knots
• Genus bounds bridge number for high distance knots
• Bridge numbers of knots in the page of an open book
• A table of genus two handlebody-knots with seven crossings
• Iterated splitting and the classification of knot tunnels