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Article Dans Une Revue Mathematische Annalen Année : 2010

Symmetric spaces of higher rank do not admit differentiable compactifications

Résumé

Any nonpositively curved symmetric space admits a topological compactification, namely the Hadamard compactification. For rank one spaces, this topological compactification can be endowed with a differentiable structure such that the action of the isometry group is differentiable. Moreover, the restriction of the action on the boundary leads to a flat model for some geometry (conformal, CR or quaternionic CR depending of the space). One can ask whether such a differentiable compactification exists for higher rank spaces, hopefully leading to some knew geometry to explore. In this paper we answer negatively.
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Dates et versions

hal-00438639 , version 1 (04-12-2009)

Identifiants

Citer

Benoit Kloeckner. Symmetric spaces of higher rank do not admit differentiable compactifications. Mathematische Annalen, 2010, 347 (4), pp.951-961. ⟨10.1007/s00208-009-0464-z⟩. ⟨hal-00438639⟩
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