Bonn Topology Group - Abstracts

General Information - Members - Activities - Topology Seminar

Talk

April 26, 2022
Kent Orr (Indiana University): Knot invariants and metabelian groups

Abstract

Metabelian knot group quotients reveal more than expected concerning 3-manifolds, knot concordance, and homology cobordism of 3-manifolds. For instance, every closed 3-manifold is a 3-fold dihedral cover branched over a knot. Metabelian invariants of knot concordance, especially Casson-Gordon invariants, provide slicing obstructions via L² and classical signatures. In this talk, I introduce and explore a new and easily computable invariant which provides necessary and sufficient conditions for a metabelian knot group quotient to extend over the group of an orientable, locally flat surface exterior in D⁴. These results hold both topologically and smoothly. I will establish numerous, perhaps surprising, equivalent characterizations of this invariant.

Back to seminar page