A combinatorial genesis of the right-angled relations in Artin's classical braid groups

2025/04/16 by Alvarado-Garduño, Omar, González, Jesús, Kahle, Matthew · 1 citation
#20F36 #55R80 #57M05 #57M15 #57Q70 (20F65 #82B26) #Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.2504.12201

Abstract

We show that the fundamental group of unlabelled configuration spaces of thick particles in either a width-2 infinite strip or a width-2 rectangle are right-angled Artin groups capturing the right-angled essence of Artin's braid groups.

Citations

• Square-section braid groups and Higman-Neumann-Neumann extensions
• On the complexity of parametrized motion planning algorithms
• The sequential (distributional) topological complexity of the ordered configuration space of disks in a strip
• The topological complexity of the ordered configuration space of disks in a strip
• Asymptotic Betti numbers for hard squares in the homological liquid regime
• Right-angled Artin groups, polyhedral products and the TC-generating function
• Configuration spaces of disks in an infinite strip
• Higher topological complexity of aspherical spaces
• The higher topological complexity of subcomplexes of products of spheres---and related polyhedral product spaces
• Higher topological complexity and its symmetrization
• Abrams's stable equivalence for graph braid groups
• On higher analogs of topological complexity
• Graph braid groups and right-angled Artin groups
• Discrete Morse theory and graph braid groups

Cited by

• Square-section braid groups and Higman-Neumann-Neumann extensions

Related

• Braid groups and right angled Artin groups
• Flat braid groups, right-angled Artin groups, and commensurability
• Embeddings of right-angled Artin groups
• Braids, trees, and operads
• Presentations of subgroups of the braid group generated by powers of band generators