Spaces of Graphs, Boundary Groupoids and the Coarse Baum-Connes Conjecture

We introduce a new variant of the coarse Baum-Connes conjecture designed to tackle coarsely disconnected metric spaces called the boundary coarse Baum-Connes conjecture. We prove this conjecture for many coarsely disconnected spaces that are known to be counterexamples to the coarse Baum-Connes conjecture. In particular, we give a geometric proof of this conjecture for spaces of graphs that have large girth and bounded vertex degree. We then connect the boundary conjecture to the coarse Baum-Connes conjecture using homological methods, which allows us to exhibit all the current uniformly discrete counterexamples to the coarse Baum-Connes conjecture in an elementary way.Comment: 27 pages, added a new section concerned with counterexamples to the conjectur

A Second Adjoint Theorem for SL(2,R)

We formulate a second adjoint theorem in the context of tempered representations of real reductive groups, and prove it in the case of SL(2,R).Comment: 38 page

On the Equivalence of Geometric and Analytic K-Homology

We give a proof that the geometric K-homology theory for finite CW-complexes defined by Baum and Douglas is isomorphic to Kasparov's K-homology. The proof is a simplification of more elaborate arguments which deal with the geometric formulation of equivariant K-homology theory.Comment: 29 pages, v4: corrected definition of E in proof of Prop 3.

Algebraic Families of Groups and Commuting Involutions

Let $G$ be a complex affine algebraic group, and let $\sigma_1$ and $\sigma_2$ be commuting anti-holomorphic involutions of $G$. We construct an algebraic family of algebraic groups over the complex projective line and a real structure on the family that interpolates between the real forms $G^{\sigma_1}$ and $G^{\sigma_2}$

Twisted Dirac Operators over Quantum Spheres

We construct new families of spectral triples over quantum spheres, with a particular attention focused on the standard Podles quantum sphere and twisted Dirac operators.Comment: 17 page

Parabolic induction and restriction via C*-algebras and Hilbert C*-modules

This paper is about the reduced group C*-algebras of real reductive groups, and about Hilbert C*-modules over these C*-algebras. We shall do three things. First we shall apply theorems from the tempered representation theory of reductive groups to determine the structure of the reduced C*-algebra (the result has been known for some time, but it is difficult to assemble a full treatment from the existing literature). Second, we shall use the structure of the reduced C*-algebra to determine the structure of the Hilbert C*-bimodule that represents the functor of parabolic induction. Third, we shall prove that the parabolic induction bimodule admits a secondary inner product, using which we can define a functor of parabolic restriction in tempered representation theory. We shall prove in the sequel to this paper that parabolic restriction is adjoint, on both the left and the right, to parabolic induction.Comment: Final version, to appear in Compositio Mathematic

Potentially dysfunctional impacts of harmonising accounting standards: the case of intangible assets

Intangible Assets as a category within accounting and reporting disclosures have become far more noticeable in recent years, including large amounts associated with brands, mastheads, franchises, and patents. Many of these items are not purchased but internally generated within the organisation, and may account for much of the difference in magnitude between book value and market capitalisation. The International Accounting Standards Committee has recently issued IAS 38 to regulate the reporting of intangible assets, and includes therein the prohibition of those intangible assets, which have been internally generated. This prohibition would cut across recently developed practices in Australia and New Zealand. The problem is compounded by an increasingly close relationship between IASs and the national standards of both Australia and New Zealand, making it very likely that the problem areas within IAS 38 will be transferred to the national standards. This paper examines the areas within IAS 38, which are likely to lead to undesirable consequences, both for internally generated intangible assets but also in terms of the reinforcement of somewhat conservative aspects of financial accounting including historical cost and the inhibiting effects on new developments generally. The possible compounding effects of an expectations gap between the traditional and expected role of financial statements is briefly examined as a possible explanation of the divergence of opinion between different groups involved in the development of accounting standards and reports

Parabolic induction, categories of representations and operator spaces

We study some aspects of the functor of parabolic induction within the context of reduced group C*-algebras and related operator algebras. We explain how Frobenius reciprocity fits naturally within the context of operator modules, and examine the prospects for an operator algebraic formulation of Bernstein's reciprocity theorem (his second adjoint theorem).Comment: 28 page

The Financial Integration of the European Union: Common and Idiosyncratic Drivers

The purpose of this paper is to establish how far the process of financial integration has gone in the European Union. There is growing evidence that the appearance of the Euro has accelerated the integration of a number of financial markets among those countries who have adopted the Euro. We identify the growth in financial integration as the process by which idiosyncratic factors at the national level become less and less important for the behaviour of particular markets. While the Euro plays an important part because it eliminates currency risk, financial integration will still emerge between other European countries as long as the institutional and legal barriers are removed.