zbMATH — the first resource for mathematics

Discrete subgroups of Lie groups: Rigidity, arithmeticity. (Sous-groupes discrets des groupes de Lie: Rigidité, arithméticité.) (French) Zbl 0835.22011
Séminaire Bourbaki. Volume 1993/94. Exposés 775-789. Paris: Société Mathématique de France, Astérisque. 227, 69-105 (Exp. No. 778) (1995).
This paper surveys recent developments in the rigidity theory of lattices in semi-simple Lie groups. Contents: Examples of lattices; Weil, Mostow and Margulis rigidity theorems and their original proofs. Arithmeticity; Matsushima’s vanishing theorem, the harmonic map proof of Margulis’ superrigidity. Extension to rank one lattices; fundamental groups of Kähler manifolds and their representation spaces.
For the entire collection see [Zbl 0811.00012].
Reviewer: P.Pansu (Paris)

22E40 Discrete subgroups of Lie groups
49Q05 Minimal surfaces and optimization
53C07 Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills)
Full Text: Numdam EuDML