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Top-dimensional
quasiflats in CAT(0) cube complexes
Jingyin Huang |
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Geometry & Topology 21 (2017) 2281–2352
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Abstract |
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We show that every –quasiflat in an –dimensional cube complex is at finite Hausdorff distance from a finite union of –dimensional orthants. Then we introduce a class of cube complexes, called weakly special cube complexes, and show that quasi-isometries between their universal covers preserve top-dimensional flats. This is the foundational result towards the quasi-isometric classification of right-angled Artin groups with finite outer automorphism group. Some of our arguments also extend to spaces of finite geometric dimension. In particular, we give a short proof of the fact that a top-dimensional quasiflat in a Euclidean building is Hausdorff close to a finite union of Weyl cones, which was previously established by Kleiner and Leeb (1997), Eskin and Farb (1997) and Wortman (2006) by different methods. |
Keywords
quasiflats, CAT(0) cube complexes, weakly special cube
complexes
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Mathematical Subject Classification 2010
Primary: 20F67
Secondary: 20F65, 20F69
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References |
Publication
Received: 10 January 2016
Revised: 17 May 2016
Accepted: 25 July 2016
Published: 19 May 2017
Proposed: Walter Neumann
Seconded: Bruce Kleiner, Dmitri Burago
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Authors |
| Jingyin Huang | |
| The Department of Mathematics and
Statistics McGill University Burnside Hall, Room 1242 805 Sherbrooke W. Montreal QC H3A 0B9 Canada |
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