Displaying similar documents to “Product preserving bundle functors on fibered manifolds.”

Product preserving bundle functors on fibered manifolds

Włodzimierz M. Mikulski (1996)

Archivum Mathematicum

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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.

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.

On the existence of prolongation of connections

Miroslav Doupovec, Włodzimierz M. Mikulski (2006)

Czechoslovak Mathematical Journal

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We classify all bundle functors G admitting natural operators transforming connections on a fibered manifold Y → M into connections on G Y → M . Then we solve a similar problem for natural operators transforming connections on Y → M into connections on G Y → Y .

On involutions of iterated bundle functors

Miroslav Doupovec, Włodzimierz M. Mikulski (2006)

Colloquium Mathematicae

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We introduce the concept of an involution of iterated bundle functors. Then we study the problem of the existence of an involution for bundle functors defined on the category of fibered manifolds with m-dimensional bases and of fibered manifold morphisms covering local diffeomorphisms. We also apply our results to prolongation of connections.