Connections on central bimodules

We define and study the theory of derivation-based connections on a recently introduced class of bimodules over an algebra which reduces to the category of modules whenever the algebra is commutative. This theory contains, in particular, a noncommutative generalization of linear connections. We also discuss the different noncommutative versions of differential forms based on derivations. Then we investigate reality conditions and a noncommutative generalization of pseudo-riemannian structures.Comment: 27 pages, AMS-LaTe

Higgs Mass and Noncommutative Geometry

We show that the description of the electroweak interactions based on noncommutative geometry of a continuous and a discrete space gives no special relations between the Higgs mass and other parameters of the model. We prove that there exists a gauge invariant term, linear in the curvature, which is trivial in the standard differential geometry but nontrivial in the case of the discrete geometry. The relations could appear only if one neglects this term, otherwise one gets the Lagrangian of the Standard model with the exact number of free parameters.Comment: 23 pages LaTeX, TPJU 4/93, (minor text misprints corrected

A bigraded version of the Weil algebra and of the Weil homomorphism for Donaldson invariants

We describe a bigraded generalization of the Weil algebra, of its basis and of the characteristic homomorphism which besides ordinary characteristic classes also maps on Donaldson invariants.Comment: 19 page

Rereading Frye: the published and unpublished works

Review of "Rereading Frye: The published and unpublished works" edited by David Boyd and Imre Salusinszk

Limit values of the non-acyclic Reidemeister torsion for knots

We consider the Reidemeister torsion associated with SL(2, C)-representations of a knot group. A bifurcation point in the SL(2, C)-character variety of a knot group is a character which is given by both an abelian SL(2, C)-representation and a non-abelian one. We show that there exist limits of the non-acyclic Reidemeister torsion at bifurcation points and the limits are expressed by using the derivation of the Alexander polynomial of the knot in this paper.Comment: to appear in Algebraic and Geometric Topolog

Exeter College, Oxford lecture

Exeter College, Oxford lectur

Letters to the Editor

Dubois Patrick. KERGOMARD (Mme Pauline). In: , . Le dictionnaire de pédagogie et d'instruction primaire de Ferdinand Buisson : répertoire biographique des auteurs. Paris : Institut national de recherche pédagogique, 2002. pp. 90-91. (Bibliothèque de l'Histoire de l'Education, 17

Non Commutative Differential Geometry, and the Matrix Representations of Generalised Algebras

The underlying algebra for a noncommutative geometry is taken to be a matrix algebra, and the set of derivatives the adjoint of a subset of traceless matrices. This is sufficient to calculate the dual 1-forms, and show that the space of 1-forms is a free module over the algebra of matrices. The concept of a generalised algebra is defined and it is shown that this is required in order for the space of 2-forms to exist. The exterior derivative is generalised for higher order forms and these are also shown to be free modules over the matrix algebra. Examples of mappings that preserve the differential structure are given. Also given are four examples of matrix generalised algebras, and the corresponding noncommutative geometries, including the cases where the generalised algebra corresponds to a representation of a Lie algebra or a $q$-deformed algebra.Comment: 16 pages Latex, No figures. Accepted for publication: Journal of Physics and Geometry, March 199

Grocer 1.0, an Econometric Toolbox for Scilab: an Econometrician Point of View

Grocer is an econometric toolbox for Scilab, a free opensource matrix- oriented toolbox similar to Matlab and Gauss. It contains more than 50 econometric different methods, with many variants and extensions. Most standard econometric tools are available. Grocer contains also two original econometric tools: a function allowing the 'automatic' estimation of the 'true model' starting from a more general and bigger one, a method that provides the most thorough expression of the so- called LSE econometric methodology; a function calculating the contributions of exogenous variables to an endogenous one.econometric software, estimation, general to specific, contributions