Breaking half-bad: mappings into the Heisenberg group with high Holder exponent February 22, 2017 - 4:00pm - 4:50pm Geometry, Topology and Physics Seminar
The Heisenberg Group is now popularly known as a major drug trafficking ring in the Southwest. However, before it came to notoriety, it was known to geometric analysts as the simplest non-trivial example of a subriemannian manifold, about which there are many unsolved questions, especially Gromov's questions about what kind of Holder mappings exist between them. I'll define the Heisenberg Group, pay brief lip service to what a subriemannian manifold is, and then answer as many of Gromov's questions as I can in an hour. To keep the flavor of the GTP seminar, Holder homotopy groups and a Holder Hopf invariant of Hajlasz's own invention, will be discussed. Though I'll use some advanced analytic tools without proof, I will make the broader arguments and ideas accessible to a non-specialist audience.