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2006 Quasiflats with holes in reductive groups
Kevin Wortman
Algebr. Geom. Topol. 6(1): 91-117 (2006). DOI: 10.2140/agt.2006.6.91

Abstract

We give a new proof of a theorem of Kleiner–Leeb: that any quasi-isometrically embedded Euclidean space in a product of symmetric spaces and Euclidean buildings is contained in a metric neighborhood of finitely many flats, as long as the rank of the Euclidean space is not less than the rank of the target. A bound on the size of the neighborhood and on the number of flats is determined by the size of the quasi-isometry constants.

Without using asymptotic cones, our proof focuses on the intrinsic geometry of symmetric spaces and Euclidean buildings by extending the proof of Eskin–Farb’s quasiflat with holes theorem for symmetric spaces with no Euclidean factors.

Citation

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Kevin Wortman. "Quasiflats with holes in reductive groups." Algebr. Geom. Topol. 6 (1) 91 - 117, 2006. https://doi.org/10.2140/agt.2006.6.91

Information

Received: 18 November 2004; Accepted: 11 August 2005; Published: 2006
First available in Project Euclid: 20 December 2017

zbMATH: 1166.20038
MathSciNet: MR2199455
Digital Object Identifier: 10.2140/agt.2006.6.91

Subjects:
Primary: 20F65
Secondary: 20G30, 22E40

Rights: Copyright © 2006 Mathematical Sciences Publishers

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