Braids, posets and orthoschemes

Abstract

In this article we study the curvature properties of the order complex of a 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.

33 pages, 16 figures

References in corpus (1)

• Combinatorial conditions that imply word-hyperbolicity for 3-manifolds

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