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

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We study flat connections in spherical Lie algebroids (over oriented compact manifolds) defined everywhere but a finite number of points. Under some assumptions concerning dimensions with any such isolated singularity we join a real number called an index. For R-spherical Lie algebroids, this index cannot be an integer. We prove the index theorem saying that the index sum is independent of the choice of a connection. Multiplying this index sum by the orientation class of M we get the Euler class of this Lie algebroid. Some integral formulae for indexes are given.