Talk:Differential calculus over commutative algebras

Additional References
There are a few references I was tempted to add, but didn't...because I was uncertain how relevant they are to the material. Instead, I will list them here in an annotated bibliography. Someone else will bear any responsibility for adding them to the article.

For the idea of a (linear) differential operators on modules over commutative rings, here are a few references:
 * A.Grothendieck, Éléments de géométrie algébrique IV, Publ. Math. 32 (IHES, Paris, 1967).
 * I.Krasil'shchik, V.Lychagin and A.Vinogradov, Geometry of Jet Spaces and Nonlinear Partial Differential Equations (Gordon and Breach, Glasgow, 1985).

The idea of connections on modules over commutative rings:
 * L.Mangiarotti and G.Sardanashvily, Connections in Classical and Quantum Field Theory (World Scientific, Singapore, 2000).
 * Eivind Eriksen, Trond S. Gustavsen, "Computing obstructions for existence of connections on modules." Eprint arXiv:math/0602616 [math.AG] 14 pages.
 * Alexander Schenkel, "Parallel transport observables for connections on finite projective modules over matrix algebras." Eprint arXiv:1201.4785 [math-ph] 9 pages.

Differential forms on modules over commutative rings:
 * G.S. Rinehart, "Differential forms on general commutative algebras". Trans. Amer. Math. Soc. 108 no. 2 (1963) 195–222.

There is probably a great deal more I have neglected, or am unaware of. —Pqnelson (talk) 18:24, 3 February 2012 (UTC)


 * See also, if anyone cares, problem 1.3 of Milnor and Stasheff's Characteristic Classess which deals with demonstrating the ring $$C^{\infty}(M)$$ completely determines the manifold $$M$$. —Pqnelson (talk) 20:41, 1 March 2012 (UTC)