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arXiv · 2406.17668

The blow-down map in Lie algebroid cohomology

Andreas Schüßler
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Abstract

We study the blow-down map in cohomology in the context of real projective blowups of Lie algebroids. Using the blow-down map in cohomology we compute the Lie algebroid cohomology of the blowup of transversals of arbitrary codimension, generalising the Mazzeo-Melrose theorem on b-cohomology. To prove the result we develop a Gysin sequence for Lie algebroids. As another example we use the developed tools to compute the Lie algebroid cohomology of the action Lie algebroid $\mathfrak{so}(3)\ltimes \mathbb{R}^3$, a result known in Poisson geometry literature. Moreover, we use similar techniques to compute the de Rham cohomology of real projective blowups.

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Andreas Schüßler. 2024-06-25. The blow-down map in Lie algebroid cohomology. https://arxiv.org/abs/2406.17668

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