Geometry & Topology seminar

Robert Young, University of Toronto

“Lipschitz spheres in the Heisenberg groups”

The (2n + 1)-dimensional Heisenberg group Hn has an invariant sub-Riemannian metric related to the standard contact structure on R2n+1, and Lipschitz maps to the Heisenberg group are closely connected to Legendrian submanifolds of R2n+1. Lipschitz maps from n- balls to Hn are abundant, but Lipschitz maps from higher-dimensional balls are rarer – any Lipschitz (n − 1)-sphere can be filled by a Lipschitz n-ball, but an n-sphere can be filled by an (n + 1)-ball only under very restrictive conditions. What about higher dimensions? In this talk, we’ll describe the Lipschitz homotopy groups of the Heisenberg group and construct fractals in Hn that fill some higher-dimensional spheres. Joint work with Stefan Wenger.