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Sur les quotients discrets de semi-groupes complexes

Christian Miebach (2010)

Annales de la faculté des sciences de Toulouse Mathématiques

Soit X = G / K un espace symétrique hermitien irréducible de type non-compact et soit S G le semi-groupe associé formé des compressions de X . Soit Γ G un sous-groupe discret. Nous donnons une condition suffisante pour que le quotient Γ S soit une variété de Stein. En outre nous démontrons qu’en général Γ S n’est pas de Stein ce qui réfute une conjecture de Achab, Betten et Krötz.

The geometry of null systems, Jordan algebras and von Staudt's theorem

Wolfgang Bertram (2003)

Annales de l’institut Fourier

We characterize an important class of generalized projective geometries ( X , X ' ) by the following essentially equivalent properties: (1) ( X , X ' ) admits a central null-system; (2) ( X , X ' ) admits inner polarities: (3) ( X , X ' ) is associated to a unital Jordan algebra. These geometries, called of the first kind, play in the category of generalized projective geometries a rôle comparable to the one of the projective line in the category of ordinary projective geometries. In this general set-up, we prove an analogue of von Staudt’s...

The proportionality constant for the simplicial volume of locally symmetric spaces

Michelle Bucher-Karlsson (2008)

Colloquium Mathematicae

We follow ideas going back to Gromov's seminal article [Publ. Math. IHES 56 (1982)] to show that the proportionality constant relating the simplicial volume and the volume of a closed, oriented, locally symmetric space M = Γ∖G/K of noncompact type is equal to the Gromov norm of the volume form in the continuous cohomology of G. The proportionality constant thus becomes easier to compute. Furthermore, this method also gives a simple proof of the proportionality principle for arbitrary manifolds.

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