Embeddability of Generalised Wreath Products

Cave, Chris; Dreesen, Dennis

doi:10.1017/s0004972714000884

Cited by 4 publications

(4 citation statements)

References 18 publications

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“…By [10], the semidirect product Γ ⋊ ∆ of Γ as above and an amenable, residually finite ∆ also admits a sequence of quotients with the desired properties. By [5], the same holds for any wreath product A ≀ Γ with abelian A (note that the published version [4] of this paper does not contain the relevant result).…”

Section: Embeddable Cones Without Property Amentioning

confidence: 76%

“…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. All these examples are coarse disjoint sums of finite Cayley graphs.…”

Section: Introductionmentioning

confidence: 98%

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Warped cones over profinite completions

Sawicki

2018

J. Topol. Anal.

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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.

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Section: Embeddable Cones Without Property Amentioning

confidence: 76%

Section: Introductionmentioning

confidence: 98%

Warped cones over profinite completions

Sawicki

2018

J. Topol. Anal.

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Section: Embeddable Cones Without Property Amentioning

confidence: 80%

Warped cones over profinite completions

Sawicki

2015

Preprint

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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.

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“…After the completion of this work, R. Tessera informed us that Theorem 1.5 can also be found in [7].…”

Section: Introductionmentioning

confidence: 99%

Lamplighter groups, median spaces and Hilbertian geometry

Genevois¹

2022

Proceedings of the Edinburgh Mathematical Society

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From any two median spaces $X$ and $Y$, we construct a new median space $X \circledast Y$, referred to as the diadem product of $X$ and $Y$, and we show that this construction is compatible with wreath products in the following sense: given two finitely generated groups $G,\,H$ and two (equivariant) coarse embeddings into median spaces $X,\,Y$, there exist a(n equivariant) coarse embedding $G\wr H \to X \circledast Y$. The construction offers a unified point of view on various questions related to the Hilbertian geometry of wreath products of groups.

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Embeddability of Generalised Wreath Products

Cited by 4 publications

References 18 publications

Warped cones over profinite completions

Warped cones over profinite completions

Warped cones over profinite completions

Lamplighter groups, median spaces and Hilbertian geometry

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