Infinite dimensional non-positively curved symmetric spaces of finite rank

Abstract

This paper concerns a study of three families of non-compact type symmetric spaces of infinite dimension. Although they have infinite dimension they have finite rank. More precisely, we show they have finite telescopic dimension. We also show the existence of Furstenberg maps for some group actions on these spaces. Such maps appear as a first step toward superrigidity results.

Some references have been added

References in corpus (3)

• Isometry groups of non-positively curved spaces: structure theory
• At infinity of finite-dimensional CAT(0) spaces
• Kähler groups, real hyperbolic spaces and the Cremona group

Cited by in corpus (8)

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• Boundary maps and maximal representations on infinite dimensional Hermitian symmetric spaces
• Furstenberg Maps For CAT(0) Targets Of Finite Telescopic Dimension
• Actions of Amenable Equivalence Relations on CAT(0) Fields
• Hyperbolic spaces, principal series and $\mathrm{O}(2,\infty )$
• The Weil-Petersson curvature operator on the universal Teichmüller space
• Representations of infinite dimension orthogonal groups of quadratic forms with finite index
• Boundaries and equivariant maps for ergodic groupoids