Mathematics > Geometric Topology
[Submitted on 13 Oct 2009]
Title:Assouad-Nagata dimension of tree-graded spaces
View PDFAbstract: Given a metric space X of finite asymptotic dimension, we consider a quasi-isometric invariant of the space called dimension function. The space is said to have asymptotic Assouad-Nagata dimension less or equal n if there is a linear dimension function in this dimension. We prove that if X is a tree-graded space (as introduced by C. Drutu and M. Sapir) and for some positive integer n a function f serves as an n-dimensional dimension function for all pieces of X, then the function 300\cdot f serves as an n-dimensional dimension function for X. As a corollary we find a formula for the asymptotic Assouad-Nagata dimension of the free product of finitely generated infinite groups: asdim_{AN} (G*H)= max\{asdim_{AN} (G), asdim_{AN} (H)\}.
Submission history
From: Jose Manuel Higes Lopez [view email][v1] Tue, 13 Oct 2009 12:24:02 UTC (10 KB)
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