High-dimensional fillings in Heisenberg groups

Details High-dimensional fillings in Heisenberg groups High-dimensional fillings in Heisenberg groups

2010-06-08

arxiv.org/abs/1006.1636v1

Mathematics

Group Theory

15 pages

Scientific paper

We use intersections with horizontal manifolds to show that high-dimensional
cycles in the Heisenberg group can be approximated efficiently by simplicial
cycles. This lets us calculate all of the higher-order Dehn functions of the
Heisenberg groups. By applying a similar technique to general nilpotent Lie
groups with lattices, we recover a Sobolev inequality of Varopoulos.

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