Volume 5, issue 2 (2001)

Download this article
For printing
Recent Issues

Volume 20
Issue 4, 1807–2438
Issue 3, 1257–1806
Issue 2, 629–1255
Issue 1, 1–627

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
Contacts
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Metric characterizations of spherical and Euclidean buildings

Ruth Charney and Alexander Lytchak

Geometry & Topology 5 (2001) 521–550

arXiv: math.MG/0106188

Abstract

A building is a simplicial complex with a covering by Coxeter complexes (called apartments) satisfying certain combinatorial conditions. A building whose apartments are spherical (respectively Euclidean) Coxeter complexes has a natural piecewise spherical (respectively Euclidean) metric with nice geometric properties. We show that spherical and Euclidean buildings are completely characterized by some simple, geometric properties.

Keywords
buildings, CAT(0) spaces, spherical buildings, Euclidean buildings, metric characterisation
Mathematical Subject Classification 2000
Primary: 20E42
Secondary: 20F65
References
Forward citations
Publication
Received: 23 November 2000
Revised: 11 May 2001
Accepted: 18 May 2001
Published: 21 May 2001
Proposed: Walter Neumann
Seconded: Jean-Pierre Otal, Steve Ferry
Authors
Ruth Charney
Mathematics Department
Ohio State University
231 West 18th Ave
Columbus
Ohio 43210
USA
Alexander Lytchak
Mathematisches Institut der Universität Bonn
Wegelerstraße 10
D-53115 Bonn
Germany