Embeddings of graph braid and surface groups in right-angled Artin groups and braid groups
Copyright policy )Embeddings of graph braid and surface groups in right-angled Artin groups and braid groups
We prove by explicit construction that graph braid groups and most surface groups can be embedded in a natural way in right-angled Artin groups, and we point out some consequences of these embedding results. We also show that every right-angled Artin group can be embedded in a pure surface braid group. On the other hand, by generalising to right-angled Artin groups a result of Lyndon for free groups, we show that the Euler characteristic -1 surface group (given by the relation x^2y^2=z^2) never embeds in a right-angled Artin group.
Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol4/agt-4-22.abs.html
- Institut de Mathématiques de Bourgogne France
- University of Burgundy France
- University of Rennes France
- University of Rennes 1 France
- Université Bourgogne Franche-Comté France
Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations, Topological methods in group theory, 20F36, surface groups, Subgroup theorems; subgroup growth, graph groups, Group Theory (math.GR), right-angled Artin group, 05C25, Fundamental groups and their automorphisms (group-theoretic aspects), FOS: Mathematics, Relations of low-dimensional topology with graph theory, graph braid group, cubed complex, graph group, graph braid groups, Braid groups; Artin groups, Graphs and abstract algebra (groups, rings, fields, etc.), 20F36, 05C25, 05C25, cube complexes, right-angled Artin groups, configuration spaces, Mathematics - Group Theory, configuration space
Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations, Topological methods in group theory, 20F36, surface groups, Subgroup theorems; subgroup growth, graph groups, Group Theory (math.GR), right-angled Artin group, 05C25, Fundamental groups and their automorphisms (group-theoretic aspects), FOS: Mathematics, Relations of low-dimensional topology with graph theory, graph braid group, cubed complex, graph group, graph braid groups, Braid groups; Artin groups, Graphs and abstract algebra (groups, rings, fields, etc.), 20F36, 05C25, 05C25, cube complexes, right-angled Artin groups, configuration spaces, Mathematics - Group Theory, configuration space
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