We study in this paper the maximal version of the coarse BaumConnes assembly map for families of expanding graphs arising from residually finite groups. Unlike for the usual Roe algebra, we show that this assembly map is closely related to the (maximal) Baum-Connes assembly map for the group and is an isomorphism for a class of expanders. We also introduce a quantitative Baum-Connes assembly ma...

The report below describes the applications of Banach KK-theory to a conjecture of P. Baum and A. Connes about the K-theory of group C∗-algebras, and a new proof of the classification by Harish-Chandra, the construction by Parthasarathy and the exhaustion by Atiyah and Schmid of the discrete series representations of connected semi-simple Lie groups. 2000 Mathematics Subject Classification: 19K...

For an orbifold X and α ∈ H(X,Z), we introduce the twisted cohomologyH c (X, α) and prove that the Connes-Chern character establishes an isomorphism between the twisted K-groups K α (X)⊗C and twisted cohomologyH c (X, α). This theorem, on the one hand, generalizes a classical result of Baum-Connes, Brylinski-Nistor, and others, that if X is an orbifold then the Chern character establishes an is...

Based on the Cayley, Grothendieck, Knudsen Mumford theory of determinants we extend the CM polarization to the Hilbert scheme. The Baum Fulton Macpherson GRR Theorem enables us to show that on any flat, proper, local complete intersection family the restriction of the extension and the original CM sheaf are isomorphic (under a mild hypothesis on the base). As a consequence the CM stability impl...

This is a survey of the relationship between C *-algebraic deformation quan-tization and the tangent groupoid in noncommutative geometry, emphasizing the role of index theory. We first explain how C *-algebraic versions of deformation quantization are related to the bivariant E-theory of Connes and Higson. With this background, we review how Weyl–Moyal quantization may be described using the ta...

In this paper, a new method for the agentification of production systems within the development of Multi-Agent-Systems (MAS) is presented.

The verification of the isomorphism conjectures of Baum and Connes and Farrell and Jones for certain classes of groups is used to compute the algebraic Kand L-theory and the topologicalK-theory of cocompact planar groups (= cocompact N.E.C-groups) and of groupsG appearing in an extension 1 → Zn → G → π → 1 where π is a finite group and the conjugation πaction on Zn is free outside 0 ∈ Zn. These...

Abstract. We reformulate the Baum-Connes conjecture with coe cients by introducing a new crossed product functor for C⇤-algebras. All confirming examples for the original Baum-Connes conjecture remain confirming examples for the reformulated conjecture, and at present there are no known counterexamples to the reformulated conjecture. Moreover, some of the known expander-based counterexamples to...

Stefan Bösner ([email protected]) Jörg Haasenritter ([email protected]) Maren Abu Hani ([email protected]) Heidi Keller ([email protected]) Andreas C Sönnichsen ([email protected]) Konstantinos Karatolios ([email protected]) Juergen R Schaefer ([email protected]) Erika Baum ([email protected]) Norber...

In the last years, a number of authors have studied the algebraic relations between the generating series of automatic sequences. It turns out that these series are solutions of Mahler type equations. This paper is mainly concerned with the difference Galois groups of Mahler type equations (these groups reflect the algebraic relations between the solutions of the equations). In particular, we s...