5,186 research outputs found
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 -homology. By the Baum/Connes
conjecture, which holds for the Bianchi groups, we obtain the -theory of
their reduced -algebras in terms of isomorphic images of the computed
-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).
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
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
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
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.
Influence of point defects on magnetic vortex structures
We employed micro-Hall magnetometry and micromagnetic simulations to
investigate magnetic vortex pinning at single point defects in individual
submicron-sized permalloy disks. Small ferromagnetic particles containing
artificial point defects can be fabricated by using an image reversal electron
beam lithography process. Corresponding micromagnetic calculations, modeling
the defects within the disks as holes, give reasonable agreement between
experimental and simulated pinning and depinning field values
A non-reflecting metamaterial slab under the finite-embedded coordinate transformation
From the explicit solutions of Maxwell's equations under the coordinate
transformation, the conditions for non-reflecting boundaries for the
two-dimensionally propagating light waves, in a finite-embedded coordinate
transformation metamaterial slab are derived in cases of extended
two-dimensional. By exploring several examples, including some reported in the
literatures and some novel developed in this study, we show that our approach
can be used to efficiently determine the condition in which a finite-embedded
coordinate transformed metamaterial slab is non-reflecting.Comment: 13 page
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