SURFACE SUBGROUPS OF RIGHT-ANGLED ARTIN GROUPS

DOI10.1142/S0218196708004536zbMath1193.20043arXiv0707.1144OpenAlexW2097437141MaRDI QIDQ3521472

Michah Sageev, John Crisp, Mark V. Sapir

Publication date: 26 August 2008

Published in: International Journal of Algebra and Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0707.1144

zbMATH Keywords

surfaceschordal graphsforbidden subgraphsright-angled Artin groupsclosed hyperbolic surface subgroupsvan-Kampen diagrams

Mathematics Subject Classification ID

Subgroup theorems; subgroup growth (20E07) Braid groups; Artin groups (20F36) Planar graphs; geometric and topological aspects of graph theory (05C10) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Topological methods in group theory (57M07) General geometric structures on low-dimensional manifolds (57M50) Fundamental group, presentations, free differential calculus (57M05) Hyperbolic groups and nonpositively curved groups (20F67) Fundamental groups and their automorphisms (group-theoretic aspects) (20F34)

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Cites Work

• Diagram groups and directed 2-complexes: homotopy and homology.
• Diagram groups are totally orderable.
• Groups of piecewise linear homeomorphisms of the real line
• Surface subgroups of Coxeter and Artin groups.
• Right-angled Artin groups are commensurable with right-angled Coxeter groups
• Embeddings of graph braid and surface groups in right-angled Artin groups and braid groups.
• A DESCRIPTION OF SOLUTIONS OF QUADRATIC EQUATIONS IN HYPERBOLIC GROUPS