"Geometry and Analysis on Groups" Research Seminar
Poincaré profile of connected Lie groups.
Romain Tessera (Université Paris-Sud)
We introduce a new family of geometric invariants for infinite graphs, and more generally metric measure spaces. Its main strength is that it is monotonous under coarse embedding. For every
-Poincaré profile is
times the maximum Cheeger constant of a subgraph of size
. We compute it for all unimodular connected Lie groups, showing that it is either polynomial or grows like
\(n/\log n\). The computation is especially interesting for rank 1 simple Lie groups. We deduce various new non-embeddability results.