Higher Divergence Functions for Heisenberg Groups

Abstract

We prove a Filling Theorem for the Heisenberg Groups $H^{2n+1}$: For a given $k$-cycle $a$ we construct a $(k+1)$-chain $b$ (the filling) with boundary $\partial b=a$ and controlled volume. For this filling $b$ we prove a uniform bound on the distance of points in $b$ to its boundary $a$. Using this we compute the higher divergence functions for the Heisenberg Groups $H^{2n+1}$. Further we generalise these results to the Jet-Groups $J^m({\mathbb{R}}^n)$ for dimension less or equal $n$ .

This paper has been withdrawn by the author due to a crucial error in the proof of the upper bounds in and below dimension n

References in corpus (1)

• High-dimensional fillings in Heisenberg groups