Isoparametric submanifolds and buildings
by
Linus Kramer
Universitaet Wuerzburg

A submanifold in euclidean space is called isoparametric if its normal bundle is globally flat, and if the spectrum of the Weingarten map is constant along any parallel normal field. A striking result of Thorbergsson says that an isoparametric submanifold of codimension at least 3 is essentially the same as a compact connected Moufang building. Recently, this result was generalized by Immervoll to codimension 2.

In this talk, I will describe the (known) connections between isoparametric submanifolds (global differential geometry) and compact buildings (topological geometry). A particularly interesting fact is that there exist infinite dimensional isoparametric submanifolds which are twin buildings associated with Kac-Moody groups (loop groups of compact Lie groups).

Date received: February 26, 2001

Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cafv-42.