Presentations of graph braid groups

DOI10.1515/form.2011.086zbMath1262.20041arXiv0907.2730OpenAlexW2950747951MaRDI QIDQ2905097

Lucas Sabalka, Daniel Scott Farley

Publication date: 24 August 2012

Published in: Forum Mathematicum (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0907.2730

zbMATH Keywords

presentationsconfiguration spacesfundamental groupsdiscrete Morse theorygraph braid groups

Mathematics Subject Classification ID

Generators, relations, and presentations of groups (20F05) Geometric group theory (20F65) Braid groups; Artin groups (20F36) Topological methods in group theory (57M07) Discriminantal varieties and configuration spaces in algebraic topology (55R80) Relations of low-dimensional topology with graph theory (57M15) Fundamental group, presentations, free differential calculus (57M05)

Related Items

Characteristics of graph braid groups ⋮ Graph of groups decompositions of graph braid groups ⋮ Topological complexity of unordered configuration spaces of certain graphs ⋮ Abrams's stable equivalence for graph braid groups ⋮ Stability phenomena in the homology of tree braid groups ⋮ Novel quantum phases on graphs using abelian gauge theory ⋮ Non-abelian quantum statistics on graphs ⋮ Geometric presentations of braid groups for particles on a graph ⋮ \(n\)-particle quantum statistics on graphs ⋮ Farley-Sabalka's Morse-theory model and the higher topological complexity of ordered configuration spaces on trees ⋮ Subdivisional spaces and graph braid groups ⋮ Negative curvature in graph braid groups

Cites Work

• Morse theory for cell complexes
• Embeddings of graph braid and surface groups in right-angled Artin groups and braid groups.
• Instabilities of robot motion
• The geometry and topology of reconfiguration
• On the cohomology rings of tree braid groups.
• Discrete Morse theory and graph braid groups.
• Embedding right-angled Artin groups into graph braid groups.
• Isotopy invariants of topological spaces