The Euler-Poincaré characteristic of a Lie algebra.

Pirashvili, Teimuraz

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

Jan Kubarski (2006)

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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...