Global theory of graded manifolds

A Global Approach to the Theory of Special Finsler Manifolds

The aim of the present paper is to provide a global presentation, as complete as we can, of the theory of special Finsler manifolds. We introduce and investigate globally (or intrinsically, free from local coordinates) many of the most important and commonly used special Finsler manifolds : locally Minkowskian, Berwald, Landesberg, general Landesberg, P -reducible, C-reducible, semi-C-reducible...

Tight Combinatorial Manifolds and Graded Betti Numbers

In this paper, we study the conjecture of Kühnel and Lutz, who state that a combinatorial triangulation of the product of two spheres S×S with j ≥ i is tight if and only if it has exactly i+2j+4 vertices. To approach this conjecture, we use graded Betti numbers of Stanley–Reisner rings. By using recent results on graded Betti numbers, we prove that the only if part of the conjecture holds when ...

Structure theory of manifolds

Global manifolds of vector elds :

For any 1 < k < n, we show how to compute the k-dimensional stable or unstable manifold of an equilibrium in a vector eld with an n-dimensional phase space. The manifold is grown as concentric (topological) (k ? 1)-spheres, which are computed as a set of intersection points of the manifold with a nite number of hyperplanes perpendicular to the last (k ?1)-sphere. These intersection points are f...

Graded Chern-Simons field theory and graded topological D-branes

We discuss graded D-brane systems of the topological A model on a Calabi-Yau threefold, by means of their string field theory. We give a detailed analysis of the extended string field action, showing that it satisfies the classical master equation, and construct the associated BV system. The analysis is entirely general and it applies to any collection of D-branes (of distinct grades) wrapping ...