College of Liberal Arts & Sciences

# Topology Seminar

Speaker:

Ben Ruppik (Max Planck Institute)

Topic:

Casson-Whitney unknotting numbers of knotted 2-spheres in the 4-sphere

**Abstract:**

This is joint work with Jason Joseph, Michael Klug, Hannah Schwartz. Any smoothly knotted 2-sphere in the 4-sphere is regularly homotopic to the unknot. This means every 2-knot in $S^4$ can be obtained by first performing a number of (trivial) finger moves on the unknot, and then removing the resulting intersection points in pairs via Whitney moves (along possibly complicated discs). We define the Casson-Whitney number of $K$ as the minimal number of finger moves needed in such a process to arrive at $K$. In this talk we will relate this to the 1-handle stabilization number, look specifically at examples of ribbon and twist-spun 2-knots and give algebraic lower bounds coming from the fundamental group.

Event Date:

November 5, 2020 - 2:30pm to 3:20pm

Location:

Online

Calendar Category:

Seminar

Seminar Category:

Geometry and Topology