Orateur
Iakovos Androulidakis
Description
This is report on work in progress with Nigel Higson. We are exploring an
idea which comes from a very simple observation: The Bruhat cells of
various flag manifolds are exactly the orbits of the action by a nilpotent
matrix group. So one might try to use the apparatus developed for singular
foliations in order to address representation theory problems. Making a
start with this, we look at the case of $CP^n$ and the action by
triangular matrices. It turns out that the nilpotency of this group allows
us to shed some geometric light in the well-known K-theory group of
$CP^n$, using index theory and techniques developed with Georges Skandalis
to split singularities. Using these techniques we also construct
interesting $K$-theory elements.
