2020
DOI: 10.1016/j.jfa.2020.108728
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Coarse Baum-Connes conjecture and rigidity for Roe algebras

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Cited by 9 publications
(21 citation statements)
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“…where Υ is the standard conditional expectation of B( 2 (Γ)) onto ∞ (Γ). (3) Then clearly a = g∈S m a g u g , as required.…”
Section: Examples Of Nonmetrizable Coarse Spacesmentioning
confidence: 90%
See 1 more Smart Citation
“…where Υ is the standard conditional expectation of B( 2 (Γ)) onto ∞ (Γ). (3) Then clearly a = g∈S m a g u g , as required.…”
Section: Examples Of Nonmetrizable Coarse Spacesmentioning
confidence: 90%
“…Therefore Lemma 4.3 implies that this graph has uniformly bounded degree, and we can find a colouring X = l−1 i=0 X i where each X i is monochromatic. Clearly, the pieces of this partition satisfy (3). A partition of Y satisfying (4) is obtained in the same exact way.…”
Section: The "Rigid" Embedding Scenariomentioning
confidence: 99%
“…n∈N has "A-by-CE" structure, namely, the coarse disjoint union [21] of the sequence (N n ) n∈N with the induced metric from the word metrics of (G n ) n∈N has Yu's property A, and the coarse disjoint union of the sequence (Q n ) n∈N with the quotient metrics coarsely embeds into Hilbert space (denoted briefly, CE), then the coarse Baum-Connes conjecture holds for the coarse disjoint union of the sequence (G n ) n∈N . It follows that the coarse Baum-Connes conjecture, and hence the coarse Novikov conjecture, holds for the relative expanders in [2], the group extensions in [3] mentioned above (see [5,23] for an alternative proof for these group extensions), and certain box spaces of free groups in [8], which do not coarsely embed into Hilbert space and yet do not coarsely contain any weakly embedded expander.…”
Section: Introductionmentioning
confidence: 87%
“…the fundamental group of a closed manifold) equipped with a word length metric, and the Gromov's zero-in-the-spectrum conjecture and the positive scalar curvature conjecture when X is a Riemannian manifold. See [55] for a comprehensive survey for the coarse Baum-Connes conjecture, and [5,9,18,19,20,21,22,24,41,48,49,50,51,53] for some recent developments.…”
Section: Introductionmentioning
confidence: 99%
“…It satisfies the strong Baum-Connes conjecture [29] which is strictly stronger than the Baum-Connes conjecture with coefficients [7], and consequently, the coarse Baum-Connes conjecture. It has been proved in [5,Proposition 2.11] by B. M. Braga, Y. C. Chung and K. Li that the second group Z 2 ≀ G (H ×F n ) constructed in [4] also satisfies the Baum-Connes conjecture with coefficients by applying a permanence result of H. Oyono-Oyono [40], and hence the coarse Baum-Connes conjecture. Since both groups are A-by-CE split extensions, our result provides an alternative proof to these facts.…”
Section: Introductionmentioning
confidence: 99%