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arXiv · 2604.01839

On the equivalence of the integrability obstructions for transitive Lie algebroids

Paolo Antonini·Alessio Giannotta
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Abstract

The integrability problem for transitive Lie algebroids can be looked at from different perspectives, revealing an interplay between cohomological methods and homotopical constructions. Mackenzie introduced a cohomological obstruction defined via sheaf-theoretic methods. On the other hand, Crainic and Fernandes used a path space approach and characterized integrability in terms of the monodromy. Recently, Meinrenken formulated the monodromy in terms of a clutching construction. We show that all of these agree. In particular, we identify the monodromy map with the Mackenzie obstruction class through the natural pairing between cohomology and homotopy.

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Paolo Antonini, Alessio Giannotta. 2026-04-02. On the equivalence of the integrability obstructions for transitive Lie algebroids. https://arxiv.org/abs/2604.01839

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