Forschungsschwerpunkt: |
Lehrstuhl für Mathematik III
Am Hubland, 97074 Würzburg Mail: kramer@mathematik.uni-wuerzburg.de Url: http://www.mathematik.uni-wuerzburg.de/~kramer/ |
Wissenschaftliche Mitglieder:
Privatdozenten:
Sonstige beteiligte Personen und Organisationen:
Forschungsschwerpunkte (und Projekte auf Basis der Grundausstattung):
CAT(0) spaces / nonpositive curvature / asymptotic cones / buildings
Ergebnisse:
The (suitably defined) geometric realization of a building
is an example of a space of nonpositive curvature in the
sense of Alexandrov. Ultraproducts of Riemannian symmetric
spaces yield in a natural way examples of such buildings;
they can be used to give new, algebraic proofs of Mostow
rigidity and of the Margulis conjecture. Using these methods,
we solve an old open question posed by Gromov on the
homeomorphism type of asymptotic cones of finitely
presented groups.
References:
L. Kramer, K. Tent, Quasi-isometric rigidity of Riemannian symmetric spaces, to appear in Proceedings Kolloquium Differentialgeometrie, Würzburg.