|Location:||MSRI: Simons Auditorium|
In this talk we will study a controlled coarse homology theory on finitely generated groups and vanishing of a particular "fundamental class" in the 0th homology group.
We will show that on any group one needs at most linear control to kill the fundamental class and that this vanishing is characterized by a certain isoperimetric inequality on the group.
We will also use invariants like type of asymptotic dimension, isoperimetric profile, isodiametric profile and decay of the heat kernel to estimate the growth necessary to kill the fundamental class.
As applications we show a link with growth of primitives of volume forms on open Riemannian manifolds and make a connection to weighted Poincare inequalities studied in the context of rigidity by P.Li and J.Wang. This is joint work with Jan Spakula (University of Muenster)