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).

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

MARKET FORCES AND CHANGES IN THE PLANT INPUT SUPPLY INDUSTRY

Agribusiness, Input Supply Industry, Fertilizer, Plant Nutrients, Seed, Capital, Market Forces, Structural Change, Porter’s Five Forces, Agribusiness, Q13, L10, L22, M22, L80,

Complexifiable characteristic classes

We examine the topological characteristic cohomology classes of complexified vector bundles. In particular, all the classes coming from the real vector bundles underlying the complexification are determined.Comment: This is the final manuscript of the author, prepared before submission to the publisher. Journal of Homotopy and Related Structures (2013) Accepted for publicatio

Accessing the cohomology of discrete groups above their virtual cohomological dimension

We introduce a method to explicitly determine the Farrell-Tate cohomology of discrete groups. We apply this method to the Coxeter triangle and tetrahedral groups as well as to the Bianchi groups, i.e. PSL_2 over the ring of integers in an imaginary quadratic number field, and to their finite index subgroups. We show that the Farrell-Tate cohomology of the Bianchi groups is completely determined by the numbers of conjugacy classes of finite subgroups. In fact, our access to Farrell-Tate cohomology allows us to detach the information about it from geometric models for the Bianchi groups and to express it only with the group structure. Formulae for the numbers of conjugacy classes of finite subgroups in the Bianchi groups have been determined in a thesis of Kr\"amer, in terms of elementary number-theoretic information on the ring of integers. An evaluation of these formulae for a large number of Bianchi groups is provided numerically in the appendix. Our new insights about the homological torsion allow us to give a conceptual description of the cohomology ring structure of the Bianchi groups

PowerAqua: fishing the semantic web

The Semantic Web (SW) offers an opportunity to develop novel, sophisticated forms of question answering (QA). Specifically, the availability of distributed semantic markup on a large scale opens the way to QA systems which can make use of such semantic information to provide precise, formally derived answers to questions. At the same time the distributed, heterogeneous, large-scale nature of the semantic information introduces significant challenges. In this paper we describe the design of a QA system, PowerAqua, designed to exploit semantic markup on the web to provide answers to questions posed in natural language. PowerAqua does not assume that the user has any prior information about the semantic resources. The system takes as input a natural language query, translates it into a set of logical queries, which are then answered by consulting and aggregating information derived from multiple heterogeneous semantic sources