Blow ups and (formal) Lie algebroid cohomology

Studying the blow-down map in cohomology in the context of real projective blow ups of Lie algebroids can be used to gain a better insight into, or even compute, Lie algebroid cohomologies, which we discuss in this talk. The key observation is that the pullback via the blow-down map is an isomorphism when restricted to flat Lie algebroid forms, which leads to the consideration of formal Lie algebroid cohomology. We introduce a spectral sequence to compute formal Lie algebroid cohomology along a submanifold and see that the pullback via the blow-down map induces a map between spectral sequences. This talk is based on joint work with Ioan Marcut.