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arXiv · 0909.4778

Braids, posets and orthoschemes

Tom Brady·Jon McCammond
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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.

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Tom Brady, Jon McCammond. 2009-09-25. Braids, posets and orthoschemes. https://doi.org/10.2140/agt.2010.10.2277

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