Work

The genus 1 bridge number of satellite knots

Year: 2025

Type: article

Abstract: Let be a satellite knot, link, or spatial graph in a 3‐manifold that is either or a lens space. Let and denote genus 0 and genus 1 bridge number, respectively. Suppose that has a companion knot (necessarily not the unknot) and wrapping number with respect to . When is not a torus knot, we show that . There are previously known counterexamples if is a torus knot. Along the way, we generalize and give a new proof of Schubert's result that . We also prove versions of the theorem applicable to when is a “lensed satellite” and when there is a torus separating components of .

Source: Journal of the London Mathematical Society

DOI: 10.1112/jlms.70260

Authors: Scott A. Taylor, Maggy Tomova

Institutions: Colby College, University of Central Florida

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Science Foundation

Awards: Collaborative Research: RUI: Connecting Spatial Graphs to Links and 3-Manifolds, Collaborative Research: RUI: Connecting Spatial Graphs to Links and 3-Manifolds