Theta-curves with unknotting number 1

Abstract: Motivated by the knotting and unknotting that can occur in biological structures like DNA and proteins, we examined when theta-curves (and knotoids) have unknotting number one. In collaboration with Ken Baker, Dorothy Buck, Allison Moore, and Scott Taylor, I have shown that unknotting number one theta-curves are prime. This is an extension of Scharlemann's theorem that all unknotting number one knots are prime. Initially one might expect the version for theta-curves to follow easily from Scharlemann’s theorem, but the situation is more subtle. In this talk I will discuss this result.

mathematical physicsalgebraic geometrygeometric topology

Audience: researchers in the topic

Richmond Geometry Meeting 2024

Series comments: The Richmond Geometry Meeting will focus on emergent research topics while bringing together researchers in algebraic geometry, low-dimensional topology, and mathematical physics. In summer 2024, we will highlight developments in Geometric Topology and Moduli.

Zoom meeting id: 835 6496 8395 password: RGMVCU2024