Given the degree sequence d of a graph, the realization graph of d is the graph having as its vertices the labeled realizations of d, with two vertices adjacent if one realization may be obtained from the other via an edge-switching operation. We describe a connection between Cartesian products in realization graphs and the canonical decomposition of degree sequences described by R.I. Tyshkevic...

We point out that the inequality det E > 0 distinguishes the kinematical phase space of canonical connection gravity from that of a gauge field theory, and characterize the eigen-vectors with positive, negative and zero-eigenvalue of the corresponding quantum operator in a lattice-discretized version of the theory. The diagonalization ofˆdet E is simplified by classifying its eigenvectors accor...

We use elliptic divisibility sequences to describe a method for estimating the global canonical height of an algebraic point on an elliptic curve. This method requires almost no knowledge of the number field or the curve, is simple to implement, and requires no factorization. The method is ideally suited to searching for algebraic points with small height, in connection with the elliptic Lehmer...

A type of almost contact hypersurfaces with Norden metric of a Kähler manifold with Norden metric is considered. The curvature tensor and the special sectional curvatures are characterized. The canonical connection on such manifolds is studied and the form of the corresponding Kähler curvature tensor is obtained. Some curvature properties of the manifolds belonging to the widest integrable main...

The canonical family of Thom forms s for 0 < s < 1 constructed by Harvey and Lawson on an oriented real vector bundle V ! X with metric connection D V is shown to have a smooth current extension to the bundle of real projective spaces, P(R V) ! X, which compactiies V in the bre directions. The current limit as r ! 1 and s ! 0 of the smooth transgression formula r ? s = r;s is the current equation

We analyse in three space-time dimensions, the connection between abelian self dual vector doublets and their counterparts containing both an explicit mass and a topological mass. Their correspondence is established in the lagrangian formalism using an operator approach as well as a path integral approach. A canonical hamiltonian analysis is presented, which also shows the equivalence with the ...

The Stickelberger elements attached to an abelian extension of number fields conjecturally participate, under certain conditions, in annihilator relations involving higher algebraic K-groups. In [13], Snaith introduces canonical Galois modules hoped to appear in annihilator relations generalising and improving those involving Stickelberger elements. In this paper we study the first of these mod...

The path integral on a homogeneous space G/H is constructed, based on the guiding principle ‘first lift to G and then project to G/H ’. It is then shown that this principle admits inequivalent quantizations inducing a gauge field (the canonical connection) on the homogeneous space, and thereby reproduces the result obtained earlier by algebraic approaches. ∗E-mail: [email protected] ...

In this paper we obtain the conditions in which two complex Finsler metrics are projective, i.e. have the same geodesics as point sets. Two important classes of such metrics are submitted to our attention: conformal projective and weakly projective complex Finsler spaces. For each of them we study the transformations of the canonical connection. We pay attention for local projectivity with a pu...

Let C → S be a proper flat family of stable curves, smooth over S0 = S r ∆. One can associate a flat family f : SUC(r, d) → S0 of moduli spaces SUCs(r, d) of semistable vector bundles of rank r and degree d with fixed determinant over the curves Cs, and also a line bundle Θ on SUC(r.d) such that its restriction to each fibre is the line bundle on SUCs(r, d) defined by the theta divisors. It is ...