Related papers: Non-Split Geometry on Products of Vector Bundles

In classical field theory, the composite fibred manifolds Y -> Z -> X provides the adequate mathematical formulation of gauge models with broken symmetries, e.g., the gauge gravitation theory. This work is devoted to connections on…

A non-zero component graph $G(\mathbb{V})$ associated to a finite vector space $\mathbb{V}$ is a graph whose vertices are non-zero vectors of $\mathbb{V}$ and two vertices are adjacent, if their corresponding vectors have at least one…

Under the hypotheses of smoothness in the coupling constant, locality, Lorentz covariance, and Poincare invariance of the deformations, combined with the preservation of the number of derivatives on each field, the consistent interactions…

We define symmetric bundles as vector bundles in the category of symmetric spaces; it is shown that this notion is the geometric analog of the one of a representation of a Lie triple system. We show that such a bundle has an underlying…

It is a classical result that any complex analytic Lie supergroup $\mathcal{G}$ is split \cite{kosz}, that is its structure sheaf is isomorphic to the structure sheaf of a certain vector bundle. However, there do exist non-split complex…

Non-split almost complex supermanifolds and non-split Riemannian supermanifolds are studied. The first obstacle for a splitting is parametrized by group orbits on an infinite dimensional vector space. Further it is shown that non-split…

We review a systematic construction of the 2-stack of bundle gerbes via descent, and extend it to non-abelian gerbes. We review the role of non-abelian gerbes in orientifold sigma models, for the anomaly cancellation in supersymmetric sigma…

We develop a semistability algorithm for vector bundles which are given as a kernel of a surjective morphism between splitting bundles on the projective space over an algebraically closed field K. This class of bundles is a generalization…

In perturbative quantum gravity, the sum of the classical Lagrangian density, a gauge fixing term and a ghost term is invariant under two sets of supersymmetric transformations called the BRST and the anti-BRST transformations. In this…

We provide several results on the existence of metrics of non-negative sectional curvature on vector bundles over certain cohomogeneity one manifolds and homogeneous spaces up to suitable stabilization. Beside explicit constructions of the…

In this paper we develop the geometry of bounded Fr\'echet manifolds. We prove that a bounded Fr\'echet tangent bundle admits a vector bundle structure. But the second order tangent bundle $T^2M$ of a bounded Fr\'echet manifold $M$, becomes…

It is shown how to sew string vertices with ghosts at tree level in order to produce new tree vertices using the Group Theoretic approach to String Theory. It is then verified the BRST invariance of the sewn vertex and shown that it has the…

We construct a vector bundle $E$ on a smooth complex projective surface $X$ with the property that the restriction of $E$ to any smooth closed curve in $X$ admits an algebraic connection while $E$ does not admit any algebraic connection.

We consider here the category of diffeological vector pseudo-bundles, and study a possible extension of classical differential geometric tools on finite dimensional vector bundles, namely, the group of automorphisms, the frame bundle, the…

We show that the BRST/anti-BRST invariant 3+1 dimensional 2-form gauge theory has further nilpotent symmetries (dual BRST /anti-dual BRST) that leave the gauge fixing term invariant. The generator for the dual BRST symmetry is analogous to…

We develop a new framework for noncommutative differential geometry based on double derivations. This leads to the notion of moment map and of Hamiltonian reduction in noncommutative symplectic geometry. For any smooth associative algebra…

This article is a continuation of math.QA/0603633 Given a strongly conformal SUSY vertex algebra V and a supercurve X we construct a vector bundle V_X on X, the fiber of which, is isomorphic to V. Moreover, the state-field correspondence of…

This study first provides a brief overview of the structure of typical Grassmann manifolds. Then a new type of supergrassmannians is construced using an odd involution in a super ringed space and by gluing superdomains together. Next,…

Let X be an irreducible smooth projective curve defined over complex numbers, S= {p_1, p_2,...,p_n} \subset X$ a finite set of closed points and N > 1 a fixed integer. For any pair (r,d) in Z X Z/N, there exists a parabolic vector bundle…

It is well-known that a (point-localized) free quantum field for massive particles with spin $s$ acting in a Hilbert space has at best scaling dimension $s+1$, which excludes its use in the perturbative construction of renormalizable…