Scott A. Taylor

collaborators

4 papers

math.GT2025

Hyperbolic Brunnian Theta Curves

Luis Celso Chan Palomo, Scott A. Taylor

A nontrivial $I^¸$ -curve in $S^{3}$ is Brunnian if each of its cycles is the unknot. We show that if the exterior of a Brunnian $I^¸$ -curve is atoroidal, then it does not contain an es…

math.GT2025

Strong Haken via Thin Position

Scott Taylor

We use thin position of Heegaard splittings to give a new proof of Haken's Lemma that a Heegaard surface of a reducible manifold is reducible and of Scharlemann's ``Strong Haken Th…

math.GT2025

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.GT2025

Closures of 1-tangles and annulus twists

Scott A. Taylor

A 1-tangle is a properly embedded arc $I ¨ $ in an unknotted solid torus $V$ in $S^{3}$ . Attaching an arc $I ¨ $ in the complementary solid torus $W$ to its endpoints creates a knot $K(Ï…