Topology Seminar

Title: New potential counterexamples to the Generalized Property R Conjecture

Speaker:  Alexander Zupan (University of Nebraska–Lincoln)

Abstract:  Kirby Problem 1.82 conjectures a characterization of n-component links in the 3-sphere which have a Dehn surgery to the connected sum of n copies of S^2 X S^1. 

This conjecture generalizes Property R, proved by Gabai in the late 1980s.  In 2010, Gompf, Scharlemann, and Thompson offered an infinite family of 2-component links which are potential counterexamples to the Generalized Property R Conjecture.  For each n, we give an infinite family of n-component possible counterexamples to the conjecture.  Notably, these links are connected to the famous Slice-Ribbon Conjecture and can be used to produce slice knots which do not appear to be ribbon.  This talk is based on joint work with Jeff Meier.