Caltech Logo

Geometry and Topology Seminar

Friday, June 8, 2018
3:00pm to 5:00pm
Add to Cal
Building 15, Room 104
Fibered, homotopy-ribbon knots and the Generalized Property R Conjecture
Jeffrey Meier, Department of Mathematics, University of Georgia,
Suppose that L is a 2-component link with an integral Dehn surgery yielding the connected sum of two copies of S^1 x S^2. How complicated can L be? Considerations of this sort fall under the purvey of the Generalized Property R Conjecture, which we will broadly overview in this talk, drawing connections with a number of open problems in low-dimensional topology. In particular, we will give many new potential counterexamples to the stronger versions of the GPRC (with relevance to the Andrews-Curtis Conjecture and the Slice-Ribbon Conjecture), while also giving an infinite family of knots that can never occur in a 2-component counterexample to the weakest version of the GPRC (with relevance to the Poincaré Conjecture). This joint work with Alex Zupan.
For more information, please contact Mathematics Department by phone at 626-395-4335 or by email at [email protected].