The genus 1 bridge number of satellite knots

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 .