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 sp...

We propose a discretization of two dimensional Euclidean Yang-Mills theories with N = 2 supersymmetry which preserves exactly both gauge invariance and an element of supersymmetry. The approach starts from the twisted form of the continuum super Yang Mills action which we show may be written in terms of two real Kähler-Dirac fields whose components transform into each other under the twisted su...

We show that the BRST operator of Neveu-Schwarz-Ramond superstring is closely related to de Rham differential on the moduli space of decorated super-Riemann surfaces P. We develop formalism where superstring amplitudes are computed via integration of some differential forms over a section of P over the super moduli space M. We show that the result of integration does not depend on the choice of...

K Kedlaya proposed an method to count the number of Fq rational points in a hyper elliptic curve using the Leschetz xed points formula in Monsky Washinitzer Cohomology The method has been extended to super elliptic curves Gaudry and G urel immediately to characteristic two hyper elliptic curves and to Cab curves J Denef F Vercauteren Based on Miura theory which is associated with how a curve is...

Talk given at the meeting Geometry and Physics on the occasion of the 65th birthday of W.M. Tulczyjew 1 1. Introduction. Geometric techniques have been applied to physics in many different ways and they have provided powerful methods of dealing with classical problems from a new geometric perspective. Vector fields, forms, exterior differential calculus, Lie groups, fibre bundles, connections, ...

The closed model category of exterior spaces, that contains the proper category, is a useful tool for the study of non compact spaces and manifolds. The notion of exterior weak N-Sequivalences is given by exterior maps which induce isomorphisms on the k-th N-exterior homotopy groups πN k for k ∈ S, where S is a set of non negative integers. The category of exterior spaces with a base ray locali...

We consider the focusing \begin{document}$ L^2 $\end{document}-supercritical Schrödinger equation in exterior of a smooth, compact, strictly convex obstacle id="M3">\begin{document}$ \Theta \subset \mathbb{R}^3 $\end{document}. We construct solution behaving asymptotically as s...

Topological relationships are the most important spatial relationships in geographical information science (GIS). There are many models of spatial relationships; the most popular model of them is 9-intersection model (9IM). There are two main problems in 9intersection model: topological paradox and linear dependency. We solve the problem of topological paradox by using the lower dimensional par...

We formulate a universal characterization of the many-particle quantum entanglement in the ground state of a topologically ordered two-dimensional medium with a mass gap. We consider a disk in the plane, with a smooth boundary of length L, large compared to the correlation length. In the ground state, by tracing out all degrees of freedom in the exterior of the disk, we obtain a marginal densit...

The notion of exterior space consists of a topological space together with a certain nonempty family of open subsets that is thought of as a ‘system of open neighborhoods at infinity’ while an exterior map is a continuous map which is ‘continuous at infinity’. The category of spaces and proper maps is a subcategory of the category of exterior spaces. In this paper we show that the category of e...