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

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