Higher Divergence Functions for Heisenberg Groups

2014/10/14 by Moritz Gruber, Gruber, Moritz
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR) #math.DG #math.GR #math.GT

paper · pdf · doi:10.48550/arxiv.1410.4064

This paper has been withdrawn by the author due to a crucial error in the proof of the upper bounds in and below dimension n

arxiv created 2015/09/29 · arxiv updated 2015/09/30

Abstract

We prove a Filling Theorem for the Heisenberg Groups H²ⁿ⁺¹: For a given k-cycle a we construct a (k+1)-chain b (the filling) with boundary ∂ 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 H²ⁿ⁺¹. Further we generalise these results to the Jet-Groups J^m(\mathbb Rⁿ) for dimension less or equal n .

Related

• Higher divergence for nilpotent groups
• Filling inequalities for nilpotent groups
• High-dimensional fillings in Heisenberg groups
• Distances in sets of positive Korányi upper density in Heisenberg Group
• The growth of the first non-Euclidean filling function of the quaternionic Heisenberg Group