# Universal spaces for asymptotic dimension zero

@inproceedings{Ma2021UniversalSF, title={Universal spaces for asymptotic dimension zero}, author={Yuankui Ma and Jeremy Siegert and Jerzy Dydak}, year={2021} }

Dranishnikov and Zarichnyi constructed a universal space in the coarse category of spaces of bounded geometry of asymptotic dimension 0. In this paper we construct universal spaces in the coarse category of separable (respectively, proper) metric spaces of asymptotic dimension 0. Our methods provide an alternative proof of Dranishnikov-Zarichnyi result.

## References

SHOWING 1-10 OF 12 REFERENCES

Universal spaces for asymptotic dimension

- Mathematics
- 2002

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…

THE COARSE CLASSIFICATION OF HOMOGENEOUS ULTRA-METRIC SPACES

- Mathematics
- 2008

We prove that two homogeneous ultra-metric spaces X, Y are coarsely equivalent if and only if Ent ♯ (X) = Ent ♯ (Y ) where Ent ♯ (X) is the so- called sharp entropy of X. This classification implies…

The coarse Baum–Connes conjecture for spaces which admit a uniform embedding into Hilbert space

- Mathematics
- 2000

Corollary 1.2. Let Γ be a finitely generated group. If Γ, as a metric space with a word-length metric, admits a uniform embedding into Hilbert space, and its classifying space BΓ has the homotopy…

Dimension zero at all scales

- Mathematics
- 2006

Abstract We consider the notion of dimension in four categories: the category of (unbounded) separable metric spaces and (metrically proper) Lipschitz maps, and the category of (unbounded) separable…

An alternative definition of coarse structures

- Mathematics
- 2006

Abstract Roe [J. Roe, Lectures on Coarse Geometry, University Lecture Series, vol. 31, Amer. Math. Soc., Providence, RI, 2003] introduced coarse structures for arbitrary sets X by considering subsets…

Lectures on coarse geometry

- Mathematics
- 2003

Metric spaces Coarse spaces Growth and amenability Translation algebras Coarse algebraic topology Coarse negative curvature Limits of metric spaces Rigidity Asymptotic dimension Groupoids and coarse…

Geometric Group Theory

- Mathematics
- 2010

The aim of this talk is to define the space of ends of a f.g. (finitely generated) group. First, define the space of ends Ends(X) for a metric space X. Define what quasi-isometries are, briefly…

The coarse classification of countable abelian groups

- Mathematics
- 2008

We classify up to coarse equivalence all countable abelian groups of finite torsion free rank. The Q-cohomological dimension and the torsion free rank are the two invariants that give us such…

Metric Spaces of Non-Positive Curvature

- Mathematics
- 1999

This book describes the global properties of simply-connected spaces that are non-positively curved in the sense of A. D. Alexandrov, and the structure of groups which act on such spaces by…