Product preserving bundle functors on fibered manifolds
The complete description of all product preserving bundle functors on fibered manifolds in terms of natural transformations between product preserving bundle functors on manifolds is given.
Product preserving bundle functors on multifibered and multifoliate manifolds.
Product preserving bundles on foliated manifolds
We present a complete description of all product preserving bundle functors on the category ℱol of all foliated manifolds and their leaf respecting maps in terms of homomorphisms of Weil algebras.
Product preserving gauge bundle functors on all principal bundle homomorphisms
Let 𝓟𝓑 be the category of principal bundles and principal bundle homomorphisms. We describe completely the product preserving gauge bundle functors (ppgb-functors) on 𝓟𝓑 and their natural transformations in terms of the so-called admissible triples and their morphisms. Then we deduce that any ppgb-functor on 𝓟𝓑 admits a prolongation of principal connections to general ones. We also prove a "reduction" theorem for prolongations of principal connections into principal ones by means of Weil functors....
Product preserving gauge bundle functors on vector bundles
A complete description is given of all product preserving gauge bundle functors F on vector bundles in terms of pairs (A,V) consisting of a Weil algebra A and an A-module V with . Some applications of this result are presented.
Projective limits of Banach vector bundles.
Prolongation of linear semibasic tangent valued forms to product preserving gauge bundles of vector bundles.
Let A be a Weil algebra and V be an A-module with dimR V < ∞. Let E → M be a vector bundle and let TA,VE → TAM be the vector bundle corresponding to (A,V). We construct canonically a linear semibasic tangent valued p-form TA,Vφ : TA,V E → ΛpT*TAM ⊗TAM TTA,VE on TA,VE → TAM from a linear semibasic tangent valued p-form φ : E → ΛpT*M ⊗ TE on E → M. For the Frolicher-Nijenhuis bracket we prove that [[TA,Vφ, TA,Vψ]] = TA,V ([[φ,ψ]]) for any linear semibasic tangent valued p- and q-forms φ and...
Prolongation of natural bundles
Prolongation of pairs of connections into connections on vertical bundles
Let be a natural bundle. We introduce the geometrical construction transforming two general connections into a general connection on the -vertical bundle. Then we determine all natural operators of this type and we generalize the result by IK̇olář and the second author on the prolongation of connections to -vertical bundles. We also present some examples and applications.
Prolongation of Poisson -form on Weil bundles
In this paper, denotes a smooth manifold of dimension , a Weil algebra and the associated Weil bundle. When is a Poisson manifold with -form , we construct the -Poisson form , prolongation on of the -Poisson form . We give a necessary and sufficient condition for that be an -Poisson manifold.
Prolongation of projectable tangent valued forms
First we deduce some general properties of product preserving bundle functors on the category of fibered manifolds. Then we study the prolongation of projectable tangent valued forms with respect to these functors and describe the complete lift of the Frölicher-Nijenhuis bracket. We also present the coordinate formula for composition of semiholonomic jets.
Prolongation of second order connections to vertical Weil bundles
We study systematically the prolongation of second order connections in the sense of C. Ehresmann from a fibered manifold into its vertical bundle determined by a Weil algebra . In certain situations we deduce new properties of the prolongation of first order connections. Our original tool is a general concept of a -field for another Weil algebra and of its -prolongation.
Prolongation of tangent valued forms to Weil bundles
We prove that the so-called complete lifting of tangent valued forms from a manifold to an arbitrary Weil bundle over preserves the Frölicher-Nijenhuis bracket. We also deduce that the complete lifts of connections are torsion-free in the sense of M. Modugno and the second author.
Prolongement des champs de vecteurs à des variétés de points proches
Prolongement des courants, positifs, fermés de masse finie.
Prolongement des structures spinorielles sur la variété des jets
Pseudo-differential operators on V-manifolds and foliations (I).
Pullback and finite coproduct preserving functors between categories of permutation representations.
Pullback and finite coproduct preserving functors between categories of permutation representations: corrigendum and addendum.