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

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dc.creatorKloeckner, Benoit
dc.date2005-06-08
dc.date.accessioned2026-07-07T12:23:50Z
dc.date.available2026-07-07T12:23:50Z
dc.descriptionIt 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.
dc.description18 p
dc.identifierhttps://arxiv.org/abs/math/0506130
dc.identifierhttp://arxiv.org/abs/math/0506130
dc.identifierGeometriae Dedicata 125 (2007) 253-270
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/214128
dc.subjectMetric Geometry
dc.subjectDifferential Geometry
dc.subject53C35
dc.titleOn differentiable compactifications of the hyperbolic plane and algebraic actions of SL(2;R) on surfaces
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