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arXiv · 1410.4064

Higher Divergence Functions for Heisenberg Groups

Moritz Gruber
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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 $n$ .

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Moritz Gruber. 2014-10-14. Higher Divergence Functions for Heisenberg Groups. https://arxiv.org/abs/1410.4064

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