Coarse Non-Amenability and Coarse Embeddings

Arzhantseva, Goulnara; Guentner, Erik; Spakula, Jan

doi:10.1007/s00039-012-0145-z

Cited by 42 publications

(82 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The first family of examples with bounded geometry was found by Arzhantseva, Guentner, and Špakula [1], and their construction was vastly generalised by Khukhro [11]. Additional examples are provided thanks to the permanence results of [5,10] due to Cave, Dreesen, and Khukhro.…”

Section: Introductionmentioning

confidence: 97%

See 1 more Smart Citation

Warped cones over profinite completions

Sawicki

2018

J. Topol. Anal.

View full text Add to dashboard Cite

Abstract. We construct metric spaces that do not have property A yet are coarsely embeddable into the Hilbert space. Our examples are so called warped cones, which were introduced by J. Roe to serve as examples of spaces nonembeddable into a Hilbert space and with or without property A. The construction provides the first examples of warped cones combining coarse embeddability and lack of property A.We also construct warped cones over manifolds with isometrically embedded expanders and generalise Roe's criteria for the lack of property A or coarse embeddability of a warped cone. Along the way, it is proven that property A of the warped cone over a profinite completion is equivalent to amenability of the group.In the appendix we solve a problem of Nowak regarding his examples of spaces with similar properties.

show abstract

Section: Introductionmentioning

confidence: 97%

“…Our construction -given an appropriate sequence of subgroups of a non-amenable group -provides an example of a warped cone that is embeddable into a Hilbert space yet does not satisfy property A. Families of such sequences are the main results of [1,10,11].…”

Section: Introductionmentioning

confidence: 99%

Warped cones over profinite completions

Sawicki

2018

J. Topol. Anal.

View full text Add to dashboard Cite

show abstract

“…• It has been already pointed out by Willett that the uniform Roe algebra C * u ( G) is not even exact if G is not amenable (see the last sentence of [AGŠ12]). This is a conclusion of the argument of [BO08, Proposition 3.7.11].…”

Section: Introductionmentioning

confidence: 99%

“…• For an appropriate choice of finite index normal subgroups of the free group F 2 , the box space F 2 coarsely embeds into a Hilbert Space, although it does not have property A (Arzhantseva, Guentner, andŠpakula [AGŠ12]). …”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A generalization of expander graphs and local reflexivity of uniform Roe algebras

Sako

2013

Journal of Functional Analysis

View full text Add to dashboard Cite

Abstract. We introduce a generalization of expander graphs, which is called a weak expander sequence. It is proved that a uniform Roe algebra of a weak expander sequence is not locally reflexive. It follows that uniform Roe algebras of expander graphs are not exact. We introduce the notion of a generalized box space to discuss box spaces and expander sequences in a unified framework. Key tools for the proof are amenable traces and measured groupoids associated with generalized box spaces.

show abstract