Bridge and pants complexities of knots

Details Bridge and pants complexities of knots Bridge and pants complexities of knots

2011-10-13

arxiv.org/abs/1110.3019v1

Mathematics

Geometric Topology

34 pages, 12 figures

Scientific paper

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.

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