Joint UGA-GT Topology Seminar at GT: Brieskorn spheres bounding rational balls

Geometry Topology Seminar
Monday, February 10, 2020 - 3:30pm for 1 hour (actually 50 minutes)
Skiles 006
Kyle Larson – UGA
Caitlin Leverson

Fintushel and Stern showed that the Brieskorn sphere Σ(2, 3, 7) bounds a rational homology ball, while its non-trivial Rokhlin invariant obstructs it from bounding an integral homology ball. It is known that their argument can be modified to show that the figure-eight knot is rationally slice, and we use this fact to provide the first additional examples of Brieskorn spheres that bound rational homology balls but not integral homology balls, including two infinite families. This is joint work with Selman Akbulut.