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Smooth manifolds and smooth functions between them. For manifolds with additional structure, see more specific tags, such as [riemannian-geometry]. For more topological aspects, see [differential-topology].

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First examples of Lie-Rinehart algebras that are not coming from Lie algebroids

Yes, there are many such Lie-Rinehart algebras. To understand such examples we need to recall some classical geometric results. Note that a $C^\infty(M)$- module is the space of global sections of a s …
Abhishek Sarkar's user avatar