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Displaying similar documents to “Integration of a density and the fiber integral for regular Lie algebroids in a nonorientable case”

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 → M over a manifold with an R -Lie algebra structure on the smooth section module and a bundle morphism γ : A → 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...

Vector form brackets in Lie algebroids

Albert Nijenhuis (1996)

Archivum Mathematicum

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A brief exposition of Lie algebroids, followed by a discussion of vector forms and their brackets in this context - and a formula for these brackets in “deformed” Lie algebroids.

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...