Geometriae Dedicata

, Volume 175, Issue 1, pp 249–256 | Cite as

Geometric density for invariant random subgroups of groups acting on CAT(0) spaces

  • Bruno DuchesneEmail author
  • Yair Glasner
  • Nir Lazarovich
  • Jean Lécureux
Original Paper


We prove that an IRS of a group with a geometrically dense action on a CAT(0) space also acts geometrically densely; assuming the space is either of finite telescopic dimension or locally compact with finite dimensional Tits boundary. This can be thought of as a Borel density theorem for IRSs.


Invariant random subgroups CAT(0) spaces Geometric density 

Mathematics Subject Classification

20F65 20P05 



Y.G. is greatfull to the hospitality of the math department at the University of Utah as well as support from Israel Science Foundation Grant ISF 441/11 and U.S. NSF Grants DMS 1107452, 1107263, 1107367 “RNMS: Geometric structures And Representation varieties” (the GEAR Network). B.D. is supported in part by Lorraine Region and Lorraine University. N.L. is supported by the Adams Fellowship Program of the Israel Academy of Sciences and Humanities.


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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • Bruno Duchesne
    • 1
    Email author
  • Yair Glasner
    • 2
  • Nir Lazarovich
    • 3
  • Jean Lécureux
    • 4
  1. 1.Institut Élie Cartan de LorraineUniversité de LorraineVandoeuvre-lès-Nancy CedexFrance
  2. 2.Department of MathematicsBen Gurion University of the NegevBeershebaIsrael
  3. 3.Mathematics DepartmentTechnion - Israel Institute of TechnologyHaifaIsrael
  4. 4.Département de Mathématiques - Bâtiment 425, Faculté des Sciences dOrsayUniversité Paris-Sud 11OrsayFrance

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