Exceptional Groups and Geometrical Structures

Basic data for this project

Description

The principal investigators studied in this project structural questions about Euclidean and spherical buildings. These geometries are metric space with upper curvature bounds which play an important role both in finite and infinite group theory. The methods in question are partly group-theoretic, and partly of a topological and geometric nature. Almost all of the questions that were addressed in the project proposal were treated successfully. In addition, we solved several new questions which turned up while we worked on the project. In somewhat more detail, the project led to a solution of an open case of the Kneser-Tits-conjecture about algebraic groups of type E8, to a conceptual proof of Serre's Center Conjecture and to a complete classification of compact Moufang buildings. In co-operational work we solved an old open problem about Lagrangian tori in hyperkähler Manifolds. Furthermore, we proved rigidity of group topologies for semi-simple Lie groups, and coarse rigidity of general Euclidean buildings. We studied embedding types for Bruhat-Tits buildings. We studied Galois descent in Euclidean buildings.