Abstract
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.
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Notes
The result is stated for proper CAT(0) spaces of finite dimension but the finite dimension assumption is used only for the boundary and not for the space itself.
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Acknowledgments
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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Duchesne, B., Glasner, Y., Lazarovich, N. et al. Geometric density for invariant random subgroups of groups acting on CAT(0) spaces. Geom Dedicata 175, 249–256 (2015). https://doi.org/10.1007/s10711-014-0038-4
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DOI: https://doi.org/10.1007/s10711-014-0038-4