Universal spaces for asymptotic dimension

By Alexander Dranishnikov, M. Zarichnyǐ. 2002

89 citations recorded by the source corpus.

Abstract We construct a universal space for the class of proper metric spaces of bounded geometry and of given asymptotic dimension. As a consequence of this result, we establish coincidence of asymptotic dimension with asymptotic inductive dimension.

Subfields: Algebra and Number Theory, Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/b4d327fe1511f6022726dc2026884a594c0b80d4

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In Algebra and Number Theory

1. Guoliang Yu
2. E. Guentner
3. Romain Tessera
4. U. Lang
5. Thilo Schlichenmaier
6. J. Dydak
7. N. Brodskiy
8. A. Mitra

In Applied Mathematics

1. S. Buyalo
2. V. Schroeder
3. U. Lang
4. Guoliang Yu
5. Romain Tessera
6. J. Dydak
7. N. Brodskiy
8. A. Mitra

In Mathematical Physics

1. Guoliang Yu
2. Romain Tessera
3. E. Guentner
4. S. Buyalo
5. U. Lang
6. V. Schroeder
7. J. Dydak
8. Thilo Schlichenmaier

Citations in the corpus

• Nagata dimension, quasisymmetric embeddings, and Lipschitz extensions (2004, result): “izes the results obtained in [16, 1.2] and [17, 4.6 and 6.5]. Acknowledgements. We thank Sergei Buyalo, Alexander Dranishnikov, Bruce Kleiner and Viktor Schroeder for inspiring discussions. Thanks to [8] we became aware of [2]. 2 Basic properties In this section we record a number of basic propertie”
• Embedding of hyperbolic groups into products of binary trees (2007, background): “There are results on the embedding of spaces into products of infinite valence trees [DJ,LS,BS1,Bu] or into products of finite unbounded valence trees [D1, DZ ,DS1].”
• Dimension zero at all scales (2006, result): “For discrete metric spaces the notion of Assouad-Nagata dimension is equivalent to the notion of asymptotic dimension of linear type considered by Gromov [9] and Roe [19] (Dranishnikov and Zarichnyi call it " asymptotic dimension with Higson property " [8]).”
• A notion of geometric complexity and its application to topological rigidity (2010, methodology): “onverse, let Xbe a (pseudo)-metric space having nite asymptotic dimension at most n. We shall show that Xhas nite decomposition complexity, indeed that X2D n. Apply the result of Drashnikov-Zarichnyi [DZ] to the nite subsets of X{ these are locally nite metric spaces and the essential observation he”