On differentiable compactifications of the hyperbolic plane and algebraic actions of SL(2;R) on surfaces - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Geometriae Dedicata Année : 2007

On differentiable compactifications of the hyperbolic plane and algebraic actions of SL(2;R) on surfaces

Résumé

It is known that the hyperbolic plane admits a countable infinity of compactifications into a closed disk such that the isometric action of SL(2;R) acts analytically on the compactified space. We prove that among those compactifications, only the two most classical ones (namely the closures of Poincaré's disk and Klein's disk) are algebraic, that is to say obtained as a union of orbits of a projectivized linear representation of SL(2;R). More generally, we classify all algebraic actions of SL(2;R) on surfaces.
Fichier principal
Vignette du fichier
article_arXiv.pdf (209.33 Ko) Télécharger le fichier
Loading...

Dates et versions

hal-00005231 , version 1 (08-06-2005)

Identifiants

Citer

Benoit Kloeckner. On differentiable compactifications of the hyperbolic plane and algebraic actions of SL(2;R) on surfaces. Geometriae Dedicata, 2007, 125, pp.253-270. ⟨hal-00005231⟩

Collections

ENS-LYON CNRS UDL
71 Consultations
46 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More