On the fiber product preserving gauge bundle functors on vector bundles

Włodzimierz M. Mikulski

Displaying similar documents to “On the fiber product preserving gauge bundle functors on vector bundles”

Product preserving gauge bundle functors on vector bundles

Włodzimierz M. Mikulski (2001)

Colloquium Mathematicae

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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 $d i m_{ℝ} (V) < \infty$ . Some applications of this result are presented.

Natural maps depending on reductions of frame bundles

Ivan Kolář (2011)

Annales Polonici Mathematici

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We clarify how the natural transformations of fiber product preserving bundle functors on $ℱ ℳ_{m}$ can be constructed by using reductions of the rth order frame bundle of the base, $ℱ ℳ_{m}$ being the category of fibered manifolds with m-dimensional bases and fiber preserving maps with local diffeomorphisms as base maps. The iteration of two general r-jet functors is discussed in detail.

On principal connection like bundles

Włodzimierz M. Mikulski (2014)

Czechoslovak Mathematical Journal

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Let $𝒫 ℬ_{m}$ be the category of all principal fibred bundles with $m$ -dimensional bases and their principal bundle homomorphisms covering embeddings. We introduce the concept of the so called $(r, m)$ -systems and describe all gauge bundle functors on $𝒫 ℬ_{m}$ of order $r$ by means of the $(r, m)$ -systems. Next we present several interesting examples of fiber product preserving gauge bundle functors on $𝒫 ℬ_{m}$ of order $r$ . Finally, we introduce the concept of product preserving $(r, m)$ -systems and describe all fiber product preserving...

On quasijet bundles

Tomáš, Jiří

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In this paper a Weil approach to quasijets is discussed. For given manifolds $M$ and $N$ , a quasijet with source $x \in M$ and target $y \in N$ is a mapping $T_{x}^{r} M \to T_{y}^{r} N$ which is a vector homomorphism for each one of the $r$ vector bundle structures of the iterated tangent bundle $T^{r}$ [, Casopis Pest. Mat. 111, No. 4, 345-352 (1986; Zbl 0611.58004)]. Let us denote by $Q J^{r} (M, N)$ the bundle of quasijets from $M$ to $N$ ; the space ${\tilde{J}}^{r} (M, N)$ of non-holonomic $r$ -jets from $M$ to $N$ is embeded into $Q J^{r} (M, N)$ . On the other hand, the bundle $Q T_{m}^{r} N$ of $(m, r)$ -quasivelocities...

The natural affinors on some fiber product preserving gauge bundle functors of vector bundles

Jan Kurek, Włodzimierz M. Mikulski (2006)

Archivum Mathematicum

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We classify all natural affinors on vertical fiber product preserving gauge bundle functors $F$ on vector bundles. We explain this result for some more known such $F$ . We present some applications. We remark a similar classification of all natural affinors on the gauge bundle functor $F^{*}$ dual to $F$ as above. We study also a similar problem for some (not all) not vertical fiber product preserving gauge bundle functors on vector bundles.