Characteristic Homomorphisms of Regular Lie Algebroids

Jan Kubarski

Displaying similar documents to “Characteristic Homomorphisms of Regular Lie Algebroids”

The Chern-Weil Homomorphism of Regular Lie Algebroids

Jan Kubarski (1991)

Publications du Département de mathématiques (Lyon)

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Integration of a density and the fiber integral for regular Lie algebroids in a nonorientable case

Urbański, Tomasz

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Characteristic classes of regular Lie algebroids – a sketch

Kubarski, Jan

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The discourse begins with a definition of a Lie algebroid which is a vector bundle $p : A \to M$ over a manifold with an $R$ -Lie algebra structure on the smooth section module and a bundle morphism $γ : A \to T M$ which induces a Lie algebra morphism on the smooth section modules. If $γ$ has constant rank, the Lie algebroid is called regular. (A monograph on the theory of Lie groupoids and Lie algebroids is published by [Lie groupoids and Lie algebroids in differential geometry (1987; Zbl 0683.53029)].) A principal...

A criterion for the minimal closedness of the Lie subalgebra corresponding to a connected nonclosed Lie subgroup.

Jan Kubarski (1991)

Revista Matemática de la Universidad Complutense de Madrid

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Vector form brackets in Lie algebroids.

Nijenhuis, A. (1996)

Archivum Mathematicum

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The Euler-Poincaré-Hopf theorem for flat connections in some transitive Lie algebroids

Jan Kubarski (2006)

Czechoslovak Mathematical Journal

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This paper is a continuation of [19], [21], [22]. We study flat connections with isolated singularities in some transitive Lie algebroids for which either $ℝ$ or $s l (2, ℝ)$ or $so (3)$ are isotropy Lie algebras. Under the assumption that the dimension of the isotropy Lie algebra is equal to $n + 1$ , where $n$ is the dimension of the base manifold, we assign to any such isolated singularity a real number called an index. For $ℝ$ -Lie algebroids, this index cannot be an integer. We prove the index theorem (the Euler-Poincaré-Hopf...