Le lundi 10 mars 2014 18:36:39 UTC+1, Nicolas M. Thiéry a écrit : > > > Yes, there is a plan which is along the lines you point out: see #10673 > > Eric's free modules are of a different nature though, since it's about > having several/may bases simultaneously and handling the changes of > bases. > > That's the point: one cannot say that the tangent space at a given point of a manifold is R^n: it is instead a generic n-dimensional vector space over R. The identification (isomorphism) with R^n relies on some specific choice of a coordinate chart (or more generally of a local frame). Hence the need for *generic* free modules, with arbitrary bases on them. Eric.
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