Braids, posets and orthoschemes

By Tom D. Brady, Jon McCammond. 2009

54 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/69c634f819279c192aa208385bd789aca9c38321

How researchers see this paper

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In Geometry and Topology

1. Damian Osajda
2. Jérémie Chalopin
3. Hiroshi Hirai
4. Victor Chepoi
5. Jingyin Huang

In Mathematical Physics

1. Damian Osajda
2. Jérémie Chalopin
3. Hiroshi Hirai
4. Victor Chepoi
5. Jingyin Huang

Citations in the corpus

• Weakly Modular Graphs and Nonpositive Curvature (2014, background): “ a 3{dimensional standard orthoscheme. An orthoscheme complex is a Euclidean simplicial complex obtained by gluing orthoschemes along common isometric faces. This notion is due to Brady and McCammond [BM10]. Moreover, as done in [BM10], the order complex of any graded poset becomes an orthoscheme co”