Braid groups and right angled Artin groups

2004/11/16 by Frank Connolly, Connolly, Frank, Margaret Doig +2 · 2 citations
Mathematics · #20F36 #57Q05(secondary) #57S30(primary) #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #math.GR #math.GT #msc:20F36

paper · pdf · doi:10.48550/arxiv.math/0411368

13 pages

arxiv created 2004/11/16 · openalex publication_date 2004/11/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The n-string braid group of a graph X is defined as the fundamental group of the n-point configuration space of the space X. This configuration space is a finite dimensional aspherical space. A. Abrams and R. Ghrist have conjectured that this braid group is a right angled Artin group if X is planar. We prove their conjecture if X is a tree whose nodes all lie in a single interval of X.

Cited by

• Braid Groups of the Sun Graph
• On the cohomology rings of tree braid groups

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