Quasiflats with holes in reductive groups

Details Quasiflats with holes in reductive groups Quasiflats with holes in reductive groups

2004-01-26

arxiv.org/abs/math/0401360v3

Algebr. Geom. Topol. 6 (2006) 91-117

Mathematics

Geometric Topology

This is the version published by Algebraic & Geometric Topology on 24 February 2006

Scientific paper

10.2140/agt.2006.6.91

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.

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