Volume 21, issue 4 (2017)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 21
Issue 5, 2557–3190
Issue 4, 1931–2555
Issue 3, 1285–1930
Issue 2, 647–1283
Issue 1, 1–645

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Subscriptions
Author Index
To Appear
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Top-dimensional quasiflats in CAT(0) cube complexes

Jingyin Huang

Geometry & Topology 21 (2017) 2281–2352
Abstract

We show that every n–quasiflat in an n–dimensional CAT(0) cube complex is at finite Hausdorff distance from a finite union of n–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 CAT(0) 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
Mathematical Subject Classification 2010
Primary: 20F67
Secondary: 20F65, 20F69
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
Authors
Jingyin Huang
The Department of Mathematics and Statistics
McGill University
Burnside Hall, Room 1242
805 Sherbrooke W.
Montreal QC H3A 0B9
Canada