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arXiv · 2407.19750

On the homotopy invariance of the twisted Lie algebroid cohomology

M. Jotz·R. Marchesini
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Abstract

Twisted Lie algebroid cohomologies, i.e. with values in representations, are shown to be Lie algebroid homotopy-invariant. Several important classes of examples are discussed. As an application, a generalized version of the Poincar\'e lemma is given in the transitive case. Together with the Mayer-Vietoris theorem, which holds in this more general context as well, this leads to a K\"unneth formula for the cohomologies of Lie algebroids with values in representations. In particular, this comprehensive paper gives a systematic way to compute explicitly the twisted Lie algebroid cohomologies of some transitive and almost transitive Lie algebroids.

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M. Jotz, R. Marchesini. 2024-07-29. On the homotopy invariance of the twisted Lie algebroid cohomology. https://arxiv.org/abs/2407.19750

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