The ($n+1$)-Lipschitz homotopy group of the Heisenberg group $\mathbb{H}^n$

Abstract

We prove that for $n\geq 2$, the Lipschitz homotopy group $\pi_{n+1}^{\rm Lip}(\mathbb{H}^n)\neq 0$ of the Heisenberg group $\mathbb{H}^n$ is nontrivial.