Classifying Space for Proper Actions and K-Theory of Group C*-algebras

By P. Baum, Alain Connes, N. Higson. 2004

614 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/019eed31a867febe50b8cf72e20cc083af4129db

How researchers see this paper

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

In Computational Theory and Mathematics

1. W. Lück
2. S. Echterhoff
3. Guoliang Yu
4. Rufus Willett
5. J. Roe
6. David Meintrup
7. J. Cuntz
8. H. Reich

In Mathematical Physics

1. Guoliang Yu
2. Rufus Willett
3. W. Lück
4. H. Reich
5. E. Guentner
6. S. Echterhoff
7. J. Tu
8. Arthur Bartels

Citations in the corpus

• Non-Hausdorff groupoids, proper actions and $K$-theory (2004, background): “The join construction ([3]) or the construction of Kasparov and Skandalis ([13, Lemma 4.”
• The Baum-Connes conjecture for hyperbolic groups (2001, background): “The Baum-Connes conjecture states that, for a discrete group G, the K-homology groups of the classifying space for proper G-action is isomorphic to the K-groups of the reduced group C-algebra of G [3, 2].”
• Identifying assembly maps in K- and L-theory (2004, background): “Connes defined a map from the K-homology of BG to the topological K-theory of C∗ r (G), and conjectured that their map induces an isomorphism for G any torsion-free discrete group (see [4] and G.”
• The Baum–Connes conjecture for free orthogonal quantum groups (2009, background): “The Baum-Connes conjecture with coefficients in A asserts that the assembly map μA : K top ∗ (G;A) → K∗(G⋉r A) is an isomorphism [6], [7].”
• Geometry of the mapping class groups I: Boundary amenability (2005, background): “As a consequence, the strong Novikov conjecture holds for Γ and hence the Novikov higher signature conjecture holds as well [ 3 , 30].”
• Survey on Classifying Spaces for Families of Subgroups (2003, background): “More information about this conjecture and its relation and application to other conjectures and problems can be found for instance in [7], [34], [57], [63], [80].”
• Going-down functors, the Künneth formula, and the Baum-Connes conjecture (2004, methodology): “We refer to [9] for a discussion on how this notion of E(G) is related to the notion of universal proper G-spaces as introduced in [3].”
• Mapping Surgery to Analysis I: Analytic Signatures (2004, background): “Kasparov and others [1,9,10] have studied a C∗-algebraic assembly map”
• Introduction To The Baum-Connes Conjecture (2002, background): “where this time the product is equipped with the product topology! Clearly G acts by isometries on EG, with finite point stabilizers (EG is a proper G-space in the sense of [9], i.”
• Higher index theory for certain expanders and Gromov monster groups I (2010, methodology): “In this section we discuss several versions of the Baum-Connes assembly map [3, 4, 5], in both the coarse and equivariant settings (a version of these assembly maps was also developed by Kasparov [25, Section 6], while the coarse geometric version appears first in work of Roe [34, Section 6.”