The Euler characteristic of any representation of a transitive Lie algebroid over a compact connected manifold vanishes unless the algebroid is the tangent bundle, in which case it equals the rank times the Euler characteristic of the manifold.
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The Euler Characteristic Of A Transitive Lie Algebroid
The Euler characteristic of any representation of a transitive Lie algebroid over a compact connected manifold vanishes unless the algebroid is the tangent bundle, in which case it equals the rank times the Euler characteristic of the manifold.