Scott A. Taylor

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math.GT2024

The genus 1 bridge number of satellite knots

Scott A. Taylor, Maggy Tomova

Let $T$ be a satellite knot, link, or spatial graph in a 3-manifold $M$ that is either $S^{3}$ or a lens space. Let $b_{0}$ and $b_{1}$ denote genus 0 and genus 1 b…

math.GT2022

Primality of theta-curves with proper rational tangle unknotting number one

Kenneth L. Baker, Dorothy Buck, Danielle O'Donnol +2

We show that if a composite $θ$ -curve has (proper rational) unknotting number one, then it is the order 2 sum of a (proper rational) unknotting number one knot and a trivial $θ$ -cu…