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

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

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

K-theory for the maximal Roe algebra of certain expanders

We study in this paper the maximal version of the coarse Baum-Connes 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 map and discuss its connections to K-theory of (maximal) Roe algebras.Comment: 45 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.

Editorial, Seminars in Cell & Developmental Biology

It is a pleasure to introduce this special edition of Cell and Development Biology dedicated to the field and application of Biosensors. This edition comprises seven reviews covering the most active research areas where we believe some of the most prominent advances in the field are likely to emerge in the near to medium term. In line with scope of this journal, some emphasis is given towards techniques applicable to Cell Biology