Homology and K-theory of the Bianchi groups

We reveal a correspondence between the homological torsion of the Bianchi groups and new geometric invariants, which are effectively computable thanks to their action on hyperbolic space. We use it to explicitly compute their integral group homology and equivariant $K$-homology. By the Baum/Connes conjecture, which holds for the Bianchi groups, we obtain the $K$-theory of their reduced $C^*$-algebras in terms of isomorphic images of the computed $K$-homology. We further find an application to Chen/Ruan orbifold cohomology. % {\it To cite this article: Alexander D. Rahm, C. R. Acad. Sci. Paris, Ser. I +++ (2011).

A refinement of a conjecture of Quillen

We present some new results on the cohomology of a large scope of SL\_2-groups in degrees above the virtual cohomological dimension; yielding some partial positive results for the Quillen conjecture in rank one. We combine these results with the known partial positive results and the known types of counterexamples to the Quillen conjecture, in order to formulate a refined variant of the conjecture

Popular education and the digital citizen: a genealogical analysis

This paper historicises and problematises the concept of the digital citizen and how it is constructed in Sweden today. Specifically, it examines the role of popular education in such an entanglement. It makes use of a genealogical analysis to produce a critical ‘history of the present’ by mapping out the debates and controversies around the emergence of the digital citizen in the 1970s and 1980s, and following to its manifestations in contemporary debates. This article argues that free and voluntary adult education (popular education) is and has been fundamental in efforts to construe the digital citizen. A central argument of the paper is that popular education aiming for digital inclusion is not a 21st century phenomenon; it actually commenced in the 1970s. However, this digitisation of citizens has also changed focus dramatically since the 1970s. During the 1970s, computers and computerisation were described as disconcerting, and as requiring popular education in order to counter the risk of the technology “running wild”. In current discourses, digitalisation is constructed in a non-ideological and post-political way. These post-political tendencies of today can be referred to as a post-digital present where computers have become so ordinary, domesticized and ubiquitous in everyday life that they are thereby also beyond criticism. (DIPF/Orig.

Some Entropy Bump Conditions for Fractional Maximal and Integral Operators

We investigate weighted inequalities for fractional maximal operators and fractional integral operators. We work within the innovative framework of "entropy bounds" introduced by Treil--Volberg. Using techniques developed by Lacey and the second author, we are able to efficiently prove the weighted inequalities.Comment: v2. Part of Theorem 1.1 from v1 was not true; we fixed the error. We thank Kabe Moen for pointing this out to u

The mod 2 cohomology rings of SL\_2 of the imaginary quadratic integers

We establish general dimension formulae for the second page of the equivariant spectral sequence of the action of the SL\_2 groups over imaginary quadratic integers on their associated symmetric space. On the way, we extend the torsion subcomplex reduction technique to cases where the kernel of the group action is nontrivial. Using the equivariant and Lyndon-Hochschild-Serre spectral sequences, we investigate the second page differentials and show how to obtain the mod 2 cohomology rings of our groups from this information.Comment: Version post-print corrigeant de petits erreurs concernant l'observation qui se r\'ef\`ere sur l'appendice, Journal of Pure and Applied Algebra, Elsevier, 2015, Accepted for publication on July 21, 201

Analytical calculation of pressure for confined atomic and molecular systems using the eXtreme-Pressure Polarizable Continuum Model

We show that the pressure acting on atoms and molecular systems within the compression cavity of the eXtreme-Pressure Polarizable Continuum method can be expressed in terms of the electron density of the systems and of the Pauli-repulsion confining potential. The analytical expression holds for spherical cavities as well as for cavities constructed from van der Waals spheres of the constituting atoms of the molecular systems