### Higher divergence of Heisenberg groups

#### Moritz Gruber (Karlsruhe & NYU)

Abstract: The m-dimensional divergence of a geodesic metric space measures the diffculty to fill a Lipschitz m-cycle which avoids a ball of radius r with an (m+1)-chain avoiding a ball of a little smaller radius $\rho r$ (for some $0 < \rho \le 1$). The asymptotic behaviour of it for $r \to \infty$ is a quasi-isometry invariant. I'm going to give an introduction to divergence before turning to the case of the higher divergence of Heisenberg groups.