Centrioles in symmetric spaces

Peter Quast (Augsburg)

The notion of a centriole in a symmetric space has
been introduced by Chen and Nagano in 1988. Centrioles
are natural generalizations of equatorial hyperspheres
in spheres to other symmetric spaces of compact type.
In the first part of our talk we describe the geometry
of centrioles and classify centrioles in simply connected
irreducible symmetric spaces of compact type in terms of
root systems.
The second part of our talk is devoted to applications of
centrioles to homotopy. Centrioles play an important role
in Bott's original proof of his famous periodicity theorem
for the homotopy of classical matrix groups. We disucss a
periodicity result for inclusions. The second part of our talk
is joint work with A.-L.Mare (University of Regina, Canada).