Braids, posets and orthoschemes

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.

PDF Access Denied

Warning: We have not been able to recognize your IP address 47.88.87.18 as that of a subscriber to this journal. Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recommendation form.

Or, visit our subscription page for instructions on purchasing a subscription. You may also contact us at contact@msp.org or by using our contact form.

Or, you may purchase this single article for USD 29.95:

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)

Tom Brady and Jon McCammond

Abstract