On Asymptotic Dimension of Groups Acting on Trees
Copyright policy )On Asymptotic Dimension of Groups Acting on Trees
We prove the following theorem: Let $��$ be the fundamental group of a finite graph of groups with finitely generated vertex groups $G_v$ having asdim $G_v\le n$ for all vertices $v$. Then asdim$��\le n+1$. This gives the best possible estimate for the asymptotic dimension of an HNN extension and the amalgamated product.
12 pages
- University of Florida United States
- University of Louisville United States
Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations, quasi-isometric spaces, Topological methods in group theory, Dimension theory in algebraic topology, asymptotic dimension, Group Theory (math.GR), 20H15, 20E34, 20F69, amalgamated free products, HNN extensions, Dimension theory in general topology, Asymptotic properties of groups, Gromov hyperbolic groups, FOS: Mathematics, Groups acting on trees, Geometric group theory, graphs of groups, Mathematics - Group Theory
Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations, quasi-isometric spaces, Topological methods in group theory, Dimension theory in algebraic topology, asymptotic dimension, Group Theory (math.GR), 20H15, 20E34, 20F69, amalgamated free products, HNN extensions, Dimension theory in general topology, Asymptotic properties of groups, Gromov hyperbolic groups, FOS: Mathematics, Groups acting on trees, Geometric group theory, graphs of groups, Mathematics - Group Theory
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