# Coarse Non-Amenability and Coarse Embeddings

@article{Arzhantseva2011CoarseNA, title={Coarse Non-Amenability and Coarse Embeddings}, author={Goulnara Arzhantseva and Erik Guentner and J{\'a}n {\vS}pakula}, journal={Geometric and Functional Analysis}, year={2011}, volume={22}, pages={22-36} }

We construct the first example of a coarsely non-amenable (= without Guoliang Yu’s property A) metric space with bounded geometry which coarsely embeds into a Hilbert space.

## 46 Citations

On non-amenable embeddable spaces in relation with free products

- Mathematics
- 2018

In this paper we give sufficient conditions for a free product of residually finite groups to admit an embeddable box space. This generalizes the constructions of Arzhantseva, Guentner and Spakula in…

Coarsely Embedding Relative Property A Groups

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We generalize relative property A for countable groups to metric spaces by considering exact families of set maps. Using exact families we show that a group which has relative property A with respect…

Coarse amenability at infinity

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We define two different weakenings of coarse amenability (also known as Yu's property A), namely fibred coarse amenability and coarse amenability at infinity. These two properties allow us to prove…

Admitting a coarse embedding is not preserved under group extensions

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We construct a finitely generated group which is an extension of two finitely generated groups coarsely embeddable into Hilbert space but which itself does not coarsely embed into Hilbert space. Our…

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In this paper, we study embeddings of uniform Roe algebras. Generally speaking, given metric spaces X and Y , we are interested in which large scale geometric properties are stable under embedding of…

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- 2011

Abstract We investigate how coarse embeddability of box spaces into Hilbert space behaves under group extensions. In particular, we prove a result which implies that a semidirect product of a…

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- 2011

The main purpose of the paper is to construct a sequence of graphs of constant degree with indefinitely growing girths admitting embeddings into $\ell_1$ with uniformly bounded distortions. This…

Uniform Local Amenability

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- 2012

The main results of this paper show that various coarse (`large scale') geometric properties are closely related. In particular, we show that property A implies the operator norm localisation…

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- 2013

We show that a bounded geometry metric space X has property A if and only if all ghost operators on X are compact.

Strong embeddability and extensions of groups

- Mathematics
- 2013

We introduce the notion of strong embeddability for a metric space. This property lies between coarse embeddability and property A. A relative version of strong embeddability is developed in terms of…

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