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

## TL;DR

This paper demonstrates that for dimensions n≥2, the Lipschitz homotopy group of the Heisenberg group is nontrivial, revealing new topological properties of these groups in geometric analysis.

## Contribution

It establishes the nontriviality of the Lipschitz homotopy group of the Heisenberg group for n≥2, a novel result in geometric topology.

## Key findings

- The Lipschitz homotopy group π_{n+1}^{Lip}(H^n) is non-zero for n≥2.
- This result provides new insights into the topological structure of the Heisenberg group.
- The paper advances understanding of Lipschitz homotopy theory in sub-Riemannian geometry.

## 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.