Braids, posets and orthoschemes

Brady, Tom; McCammond, Jon

doi:10.2140/agt.2010.10.2277

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Braids, posets and orthoschemes

Tom Brady and Jon McCammond

Algebraic & Geometric Topology 10 (2010) 2277–2314

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.

Keywords

braid group, Artin group, poset, orthoscheme, nonpositive curvature

Mathematical Subject Classification 2000

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

Secondary: 06A11

References

Publication

Received: 25 September 2009

Revised: 21 July 2010

Accepted: 26 August 2010

Published: 26 November 2010

Authors

Tom Brady
School of Mathematical Sciences Dublin City University Glasnevin, Dublin 9 Ireland
http://webpages.dcu.ie/~bradyt/
Jon McCammond
Department of Mathematics University of California Santa Barbara CA 93106 USA
http://www.math.ucsb.edu/~jon.mccammond

Volume 10, issue 4 (2010)