Complexes of groups and geometric small cancelation over graphs of groups

Abstract We study Artin kernels, i.e. kernels of discrete characters of right-angled Artin groups, and we show that they decompose as graphs of groups in a way that can be explicitly computed from the underlying graph. When the underlying graph is chordal, we show that every such subgroup either surjects to an infinitely generated free group or is a generalized Baumslag–Solitar group of variable rank. In particular, for block graphs (e.g. trees), we obtain an explicit rank formula and discuss some features of the space of fibrations of the associated right-angled Artin group.

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A criterion for residual 𝑝-finiteness of arbitrary graphs of finite 𝑝-groups

Journal of Group Theory ◽

10.1515/jgth-2018-0205 ◽

2019 ◽

Vol 22 (5) ◽

pp. 837-844

Author(s):

Gareth Wilkes

Keyword(s):

Fundamental Group ◽

Infinite Graphs ◽

Graphs Of Groups ◽

Arbitrary Graphs

Abstract We establish conditions under which the fundamental group of a graph of finite p-groups is necessarily residually p-finite. The technique of proof is independent of previously established results of this type, and the result is also valid for infinite graphs of groups.

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Non-positively curved complexes of groups and boundaries

Geometry & Topology ◽

10.2140/gt.2014.18.31 ◽

2014 ◽

Vol 18 (1) ◽

pp. 31-102 ◽

Cited By ~ 8

Author(s):

Alexandre Martin

Keyword(s):

Positively Curved ◽

Complexes Of Groups

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Quasi-isometric rigidity for graphs of virtually free groups with two-ended edge groups

Journal für die reine und angewandte Mathematik (Crelles Journal) ◽

10.1515/crelle-2021-0067 ◽

2021 ◽

Vol 0 (0) ◽

Author(s):

Sam Shepherd ◽

Daniel J. Woodhouse

Keyword(s):

Free Group ◽

Large Family ◽

Finitely Generated ◽

Free Vertex ◽

Cyclic Subgroups ◽

Graphs Of Groups ◽

Jsj Decomposition ◽

Finitely Generated Groups ◽

Hnn Extensions ◽

Abelian Subgroups

Abstract We study the quasi-isometric rigidity of a large family of finitely generated groups that split as graphs of groups with virtually free vertex groups and two-ended edge groups. Let G be a group that is one-ended, hyperbolic relative to virtually abelian subgroups, and has JSJ decomposition over two-ended subgroups containing only virtually free vertex groups that are not quadratically hanging. Our main result is that any group quasi-isometric to G is abstractly commensurable to G. In particular, our result applies to certain “generic” HNN extensions of a free group over cyclic subgroups.

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