Equivariant E-Theory for C*-Algebras

By E. Guentner, N. Higson, J. Trout. 2000

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Groups acting properly on “bolic” spaces and the Novikov conjecture (2003, methodology): “Γ,B)) → RKΓ i(EΓ,B). It is easy to see that βB◦ αis the identity of Ki(C∗(Γ,B)). But the fact that the composition α◦βB is also the identity in the case of a discrete group Γ is more complicated (cf. [GHT]). Suﬃcient conditions for the injectivity of the Baum-Connes map To establish the injectivity ”
The Novikov conjecture and geometry of Banach spaces (2012, background): “The fact that C(Z)⊗̂A(X)⊗̂A is a Γ-proper C∗-algebra implies that μ2 is an isomorphism (it can be seen by the Mayer-Vietoris and five lemma argument [9]).”
Permanence properties of the Baum-Connes conjecture (2001, methodology): “For discrete G, this map has been studied by Guentner, Higson and Trout in [11] (in the frame of E-theory), where they showed that it is an isomorphism if H is finite.”
Equivariant Kasparov theory and generalized homomorphisms (2000, background): “Our definition of a stable homotopy functor is equivalent to the definitions in [8] and in [21].”