Books on differential geometry on Banach Spaces.

AI Thread Summary
The discussion centers on recommendations for books and preprints related to the study of Banach manifolds and differential geometry (DG) in a broader context. Participants suggest "The Convenient Setting for Global Analysis," which focuses on infinite-dimensional manifolds, as a valuable resource. There is a consensus on the need for textbooks that cover more general geometric objects beyond standard courses in differential geometry, with Banach manifolds being a key area of interest. Additional recommendations include Lang's "Fundamentals of Differential Geometry" and Abraham, Marsden, and Ratiu's "Manifolds, Tensor Analysis and Applications," which are noted for their comprehensive treatment of the subject. The conversation reflects a quest for deeper understanding and resources in advanced geometric studies.
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Can you recommend me of books or preprints that cover reasonabely well this topic?

Thanks.
 
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Do you mean the basic study of Banach manifolds h(ttp://en.wikipedia.org/wiki/Banach_manifold)?

In any case, it cannot hurt for you to take a look at the book (free online) "The convenient setting for global analysis" which is a book about infinite dimensional manifolds.
 
Basically I am looking for DG on a more general setting than the one covered in any first course in DG, I guess Hilbert spaces and banach spaces comes next after the real space.

I'll check the book.
 
Well, I now find myself in similar circumstances. I want a textbook on the most general geometric objects possible, but I don't know how much more general you can get then Banach manifolds. I guess the algebraic stuff?
 
Lang's "Fundamentals of Differential Geometry"

And Abraham/Marsden/Ratiu's "Manifolds, Tensor Analysis and applications"
 

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