The coarse Baum–Connes conjecture and groupoids

By G. Skandalis, J. Tu, Guoliang Yu. 2002

83 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/a39d4341f3abae1a599996f9848e73b239a7feb2

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Rufus Willett
2. Ján Špakula
3. E. Guentner
4. P. Xu
5. Marius Dadarlat
6. N. Brown
7. C. Laurent-Gengoux
8. J. Tu

In Applied Mathematics

1. Rufus Willett
2. E. Guentner
3. Mark V. Sapir
4. Ján Špakula
5. Marius Dadarlat
6. Denis V. Osin
7. C. Laurent-Gengoux
8. P. Xu

In Mathematical Physics

1. Rufus Willett
2. E. Guentner
3. Ján Špakula
4. Nathanial P. Brown Narutaka Ozawa
5. Denis V. Osin
6. Marius Dadarlat
7. P. Xu
8. A. Ol’shanskii

Citations in the corpus

• Squeezing and Higher Algebraic K-Theory (2003, background): “Later on the Novikov conjecture was established for groups of finite asymptotic dimension ([Hig00]) and groups admitting a uniform embedding ([STY02]), irrespective of finiteness or otherwise of BΓ.”
• Uniform embeddings of bounded geometry spaces into reflexive Banach space (2003, background): “Gromov introduced the notion of uniform embeddability and later suggested that uniform embeddability of a discrete group into a Hilbert space, or even into a uniformly convex Banach space, might be relevant for applications to the Novikov conjecture [3, 2]. Yu subsequently proved the Coarse Baum-Con”
• Higher index theory for certain expanders and Gromov monster groups I (2010, unknown): “The referee has pointed out to us that this can also be proved using the groupoid point of view on the coarse Baum-Connes conjecture [38].”
• Amenability and exactness for dynamical systems and their C*-algebras (2000, unknown): “Recall that the Strong Novikov Conjecture with coecients holds for every nitely generated group that admits a uniform embedding into a Hilbert space ([Yu], [Hi], [ STY ]).”
• Uniform embeddability of relatively hyperbolic groups (2005, background): “(A condition on finiteness of the classifying space was later removed [ 14 ].)”
• Exactness and the Novikov conjecture (2000, background): “is injective. Answering a question of Gromov, Yu proved the following theorem [15, 11 ].”
• Maximal and reduced Roe algebras of coarsely embeddable spaces (2011, background): “Next, it is shown in [24] that property A of X corresponds to (topological) amenability of G (X) and in [25] that coarse embeddability of X into a Hilbert space corresponds to the Haagerup property for G (X).”
• Lacunary hyperbolic groups (2007, background): “ng Novikov Conjecture (that is the Baum-Connes assembly map with trivial coefficients is injective) since all direct limits of hyperbolic groups satisfy that conjecture (hyperbolic groups satisfy it by [STY], and direct limits respect the conjecture by [Ro, Proposition 2.4]). It is also easy to see th”
• Twisted K theory of differentiable stacks (2003, methodology): “oupoid Γ, the Baum-Connes map µ r: K top ∗ (Γ) →K∗(C∗(Γ)) can be used to study the K-theory groups of C∗(Γ). The above map generalizes both the assembly map for groups [7] and the coarse assembly map [67]. Of course, many techniques used to study the Baum-Connes conjecture for groups [35] can be ext”