Displaying similar documents to “Holonomicity in synthetic differential geometry of jet bundles.”

On topological invariants of vector bundles

Zbigniew Szafraniec (1992)

Annales Polonici Mathematici

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Let E → W be an oriented vector bundle, and let X(E) denote the Euler number of E. The paper shows how to calculate X(E) in terms of equations which describe E and W.

On the functorial prolongations of principal bundles

Ivan Kolář, Antonella Cabras (2006)

Commentationes Mathematicae Universitatis Carolinae

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We describe the fundamental properties of the infinitesimal actions related with functorial prolongations of principal and associated bundles with respect to fiber product preserving bundle functors. Our approach is essentially based on the Weil algebra technique and an original concept of weak principal bundle.

Continuity of projections of natural bundles

Włodzimierz M. Mikulski (1992)

Annales Polonici Mathematici

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This paper is a contribution to the axiomatic approach to geometric objects. A collection of a manifold M, a topological space N, a group homomorphism E: Diff(M) → Homeo(N) and a function π: N → M is called a quasi-natural bundle if (1) π ∘ E(f) = f ∘ π for every f ∈ Diff(M) and (2) if f,g ∈ Diff(M) are two diffeomorphisms such that f|U = g|U for some open subset U of M, then E(f)|π^{-1}(U) = E(g)|π^{-1}(U). We give conditions which ensure that π: N → M is continuous. In particular,...

Higher order connections.

Eastwood, Michael G. (2009)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

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Natural transformations between T²₁T*M and T*T²₁M

Miroslav Doupovec (1991)

Annales Polonici Mathematici

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We determine all natural transformations T²₁T*→ T*T²₁ where T k r M = J 0 r ( ℝ k , M ) . We also give a geometric characterization of the canonical isomorphism ψ₂ defined by Cantrijn et al.

On special types of nonholonomic 3 -jets

Ivan Kolář (2012)

Archivum Mathematicum

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We deduce a classification of all special types of nonholonomic 3 -jets. In the introductory part, we summarize the basic properties of nonholonomic r -jets.

On 2-distributions in 8-dimensional vector bundles over 8-complexes

Martin Čadek, Jiří Vanžura (1996)

Colloquium Mathematicae

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It is shown that the ℤ 2 -index of a 2-distribution in an 8-dimensional spin vector bundle over an 8-complex is independent of the 2-distribution. Necessary and sufficient conditions for the existence of 2-distributions in such vector bundles are given in terms of characteristic classes and a certain secondary cohomology operation. In some cases this operation is computed.