High-dimensional fillings in Heisenberg groups

Robert Young

Published 2010-06-08, updated 2012-10-23Version 2

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, thus proving a conjecture of Gromov.