109 research outputs found
On the Baum-Connes conjecture for groups acting on CAT(0)-cubical spaces
No full textWe give a new proof of the Baum–Connes conjecture with coefficients for any second countable, locally compact topological group that acts properly and cocompactly on a finite-dimensional CAT(0)-cubical space with bounded geometry. The proof uses the Julg–Valette complex of a CAT(0)-cubical space introduced by the 1st three authors and the direct splitting method in Kasparov theory developed by the last author
A differential complex for CAT(0) cubical spaces
No full textIn the 1980's Pierre Julg and Alain Valette, and also Tadeusz Pytlik and Ryszard Szwarc, constructed and studied a certain Fredholm operator associated to a simplicial tree. The operator can be defined in at least two ways: from a combinatorial flow on the tree, similar to the flows in Forman's discrete Morse theory, or from the theory of unitary operator-valued cocycles. There are applications of the theory surrounding the operator to C⁎-algebra K-theory, to the theory of completely bounded representations of groups that act on trees, and to the Selberg principle in the representation theory of p-adic groups. The main aim of this paper is to extend the constructions of Julg and Valette, and Pytlik and Szwarc, to CAT(0) cubical spaces. A secondary aim is to illustrate the utility of the extended construction by developing an application to operator K-theory and giving a new proof of K-amenability for groups that act properly on finite dimensional CAT(0)-cubical spaces
A proof of the Baum-Connes conjecture for -adic
No full textWe give a proof of the Baum-Connes conjecture for p-adic GL(n).</p
Spaces with Vanishing ^2ehBHomology and their Fundamental Groups (after Farber and Weinberger)
No full textWe characterize those groups which can occur as the fundamental groups of finite CW-complexes with vanishing ^2ehBhomology (the first examples of such groups were obtained by Farber and Weinberger)
Property A and affine buildings
No full textYu's Property A is a non-equivariant generalisation of amenability introduced in his study of the coarse Baum Connes conjecture. In this paper we show that all affine buildings of type A2, B2 and G2 have Property A. Together with results of Guentner, Higson and Weinberger, this completes a programme to show that all affine building have Property A. In passing we use our technique to obtain a new proof for groups acting on buildings.The author was supported by EPSRC postdoctoral fellowship EP/C53171X/1.<br/
Categories of fractions and excision in KK-theory
No full textAbstractUsing elementary ideas from the theory of categories of fractions, we construct bivariant homology/cohomology groups E(A, B) for C∗-algebras, which satisfy general excision axioms, and are equal to Kasparov's groups KK(A, B) for nuclear (or more generally K-nuclear) C∗-algebras
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