Bridge and pants complexities of knots

Abstract

We modify an approach of Johnson to define the distance of a bridge splitting of a knot in a 3-manifold using the dual curve complex and pants complex of the bridge surface. This distance can be used to determine a complexity, which becomes constant after a sufficient number of stabilizations and perturbations, yielding an invariant of the manifold-knot pair. We also give evidence toward the relationship between the pants distance of a bridge splitting and the hyperbolic volume of the exterior of a knot.

34 pages, 12 figures

Cited by in corpus (8)

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• Bridge trisections of knotted surfaces in 4--manifolds
• Isotopies of surfaces in 4-manifolds via banded unlink diagrams
• Kirby-Thompson distance for trisections of knotted surfaces
• Essential surfaces in highly twisted link complements
• Uniqueness of higher genus bridge surfaces for torus knots
• Bounding the Kirby-Thompson invariant of spun knots
• Bridge trisections and Seifert solids