Braids, posets and orthoschemes

Brady, Tom¹ ; McCammond, Jon²

¹School of Mathematical Sciences, Dublin City University, Glasnevin, Dublin 9, Ireland
²Department of Mathematics, University of California, Santa Barbara CA 93106, USA

Algebraic and Geometric Topology, Tome 10 (2010) no. 4, pp. 2277-2314

Résumé

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.

Détail

DOI : 10.2140/agt.2010.10.2277

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

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