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Asymptotic Dimension of Finitely Presented Groups [PDF]
Proceedings of the American Mathematical Society, 2008 It is proven that if a finitely presented group is one ended it has asymptotic dimension bigger than one. It follows that finitely presented groups with asdim 1 are virtually free. A counterexample is given for the finitely generated case.
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On the Asymptotic Extension Dimension [PDF]
Ukrainian Mathematical Journal, 2011 We introduce an asymptotic counterpart of the extension dimension defined by Dranishnikov. The main result establishes the relationship between the asymptotic extensional dimension of a proper metric space and the extension dimension of its Higson corona.
Dušan Repovš, M Zarichnyi
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Buildings Have Finite Asymptotic Dimension [PDF]
Russian Journal of Mathematical Physics, 2009 4 pages; v2: typos corrected, to appear in Russian Journal of Mathematical Physics, special issue in honour of Nicolai Teleman v3: minor confusions of geometric/combinatorial aspects ...
Thomas Schick
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Strongly sublinear separators and bounded asymptotic dimension for sphere intersection graphs
International Symposium on Computational GeometryIn this paper, we consider the class $\mathcal{C}^d$ of sphere intersection graphs in $\mathbb{R}^d$ for $d \geq 2$. We show that for each integer $t$, the class of all graphs in $\mathcal{C}^d$ that exclude $K_{t,t}$ as a subgraph has strongly sublinear
James Davies +3 more
semanticscholar +1 more source
2017
This chapter considers the notion of asymptotic dimension. It first provides an overview of asymptotic dimension before explaining the asymptotic dimensions of free abelian and nonabelian groups, free groups, groups, integers, metric spaces, and products.
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This chapter considers the notion of asymptotic dimension. It first provides an overview of asymptotic dimension before explaining the asymptotic dimensions of free abelian and nonabelian groups, free groups, groups, integers, metric spaces, and products.
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Higson Corona and Asymptotic Dimension
, 2018In this chapter we review the construction of the Higson compactification (and corona) and the concept of asymptotic dimension for metric spaces.
J. A. Álvarez López, A. Candel
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Asymptotic Hereditary Asphericity of Metric Spaces of Asymptotic Dimension 1
Topology and Its Applications, 2010 \textit{T. Januszkiewicz} and \textit{J. Świątkowski} introduced the concept of asymptotic hereditary asphericity (AHA) [in Geom. Topol. 11, 727-758 (2007; Zbl 1188.20043)]. Using this property, they showed that there exist hyperbolic groups of arbitrary cohomological dimension containing no subgroups isomorphic to fundamental groups of closed ...
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