Exceptional Groups and Geometrical Structures

• Antragsteller: Professor Dr. Linus Kramer
• Fachliche Zuordnung: Mathematik
• Förderung: Förderung von 2010 bis 2013
• Projektkennung: Deutsche Forschungsgemeinschaft (DFG) - Projektnummer 179484142

• Erstellungsjahr: 2013

Zusammenfassung der Projektergebnisse

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.

Projektbezogene Publikationen (Auswahl)

• Coarse equivalences of Euclidean buildings. Adv. Math.
  L. Kramer and R. M. Weiss
  
• The topology of a semisimple Lie group is essentially unique, Adv. Math. 228 (2011), no. 5, 2623–2633
  L. Kramer
  
• Compact totally disconnected Moufang buildings, Tohoku Math. J. (2) 64 (2012), no. 3, 333–360
  T. Grundhöfer et al.
  
• On intertwining implies conjugacy for classical groups, 2012
  D. Skodlerack
  
• The Kneser-Tits conjecture for groups with Tits-index E66/8,2 over an arbitrary field, Transform. Groups 17 (2012), no. 1, 209–231
  R. Parimala, J.-P. Tignol and R. M. Weiss
  
• Field embeddings which are conjugate under a p-adic classical group. Manuscripta Mathematica, 2013
  D. Skodlerack
  (Siehe online unter https://doi.org/10.1007/s00229-013-0654-6)
• Local identification of spherical buildings and finite simple groups of Lie type, Math. Proc. Cambridge Philos. Soc. 154 (2013), no. 3, 527–547
  U. Meierfrankenfeld, G. Stroth and R. M. Weiss
  (Siehe online unter https://doi.org/10.1017/S0305004113000078)
• Receding polar regions of a spherical building and the center conjecture, Ann. Inst. Fourier 63 (2013), 479-513
  B. Mühlherr and R. M. Weiss
  
• The centralizer of a classical group and Bruhat Tits buildings. Annales de l’Institut Fourier, 63(2):515–546, 2013
  D. Skodlerack
  
• Webs of Lagrangian tori in projective symplectic manifolds, Invent. Math. 192 (2013), no. 1, 83–109
  J.-M. Hwang and R. M. Weiss