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2010 Braids, posets and orthoschemes
Tom Brady, Jon McCammond
Algebr. Geom. Topol. 10(4): 2277-2314 (2010). DOI: 10.2140/agt.2010.10.2277

Abstract

In this article we study the curvature properties of the order complex of a bounded graded poset under a metric that we call the “orthoscheme metric”. In addition to other results, we characterize which rank 4 posets have CAT(0) orthoscheme complexes and by applying this theorem to standard posets and complexes associated with four-generator Artin groups, we are able to show that the 5–string braid group is the fundamental group of a compact nonpositively curved space.

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Tom Brady. Jon McCammond. "Braids, posets and orthoschemes." Algebr. Geom. Topol. 10 (4) 2277 - 2314, 2010. https://doi.org/10.2140/agt.2010.10.2277

Information

Received: 25 September 2009; Revised: 21 July 2010; Accepted: 26 August 2010; Published: 2010
First available in Project Euclid: 19 December 2017

zbMATH: 1205.05246
MathSciNet: MR2745672
Digital Object Identifier: 10.2140/agt.2010.10.2277

Subjects:
Primary: 05E15, 06A06, 20F36, 20F65, 51M20
Secondary: 06A11

Rights: Copyright © 2010 Mathematical Sciences Publishers

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