Large scale geometry is the study of geometric objects viewed from a great distance. The
idea of large scale geometry can be traced back to Mostow's work on rigidity and the work of …

The asymptotic dimension theory was founded by Gromov [M. Gromov, Asymptotic invariants
of infinite groups, in: Geometric Group Theory, vol. 2, Sussex, 1991, in: London Math. Soc …

We investigate a variant of Gromov's notion of asymptotic dimension that was introduced
and named Nagata dimension by Assouad. This turns out to be a quasisymmetry invariant of …

arXiv:2112.10681v2 [math.MG] 1 Jul 2022 Page 1 MAPPING CLASS GROUPS ARE
QUASICUBICAL HARRY PETYT Abstract. It is proved that the mapping class group of any closed …

Universal spaces for asymptotic dimension Page 1 Topology and its Applications 140 (2004)
203–225 www.elsevier.com/locate/topol Universal spaces for asymptotic dimension A …

Asymptotic dimension of relatively hyperbolic groups Page 1 IMRN International
Mathematics Research Notices 2005, No. 35 Asymptotic Dimension of Relatively …

We show that an infinite weighted tree admits a bi-Lipschitz embedding into Hilbert space if
and only if it does not contain arbitrarily large complete binary trees with uniformly bounded …

Embedding of hyperbolic groups into products of binary trees Page 1 DOI: 10.1007/s00222-007-0045-2
Invent. math. 169, 153–192 (2007) Embedding of hyperbolic groups into products of binary …

For a large class of metric spaces X including discrete groups we prove that the asymptotic
Assouad–Nagata dimension AN-asdimX of X coincides with the covering dimension dim …

The notion of the decomposition complexity was introduced in [14] using a game theoretic
approach. We introduce a notion of straight decomposition complexity and compare it with …