Geometry, Topology and Dynamics Seminar
Dirk Toeben
Cologne University
Equivariant LS-category of polar actions
Abstract: Equivariant LS-category of a G-space X is the least number of G-equivariant, G-contractible open sets
required to cover X. It is a measure of the topological complexity of X as a G-space. In this work, joint
with Steve Hurder, we obtain a lower bound on the equivariant LS-category for arbitrary proper G-spaces
in terms of the stratification by orbit types. A G-action is polar if it admits a complete section. We obtain
an upper bound for proper polar actions in terms of the equivariant LS-category of its generalized Weyl
group. As an application we reprove a theorem of Singhof that determines the classical Lusternik-
Schnirelmann category for the Lie groups $U(n)$ and $SU(n)$.
Monday September 24, 2007 at 3:00 PM in SEO 512