Books on differential geometry on Banach Spaces.

[MathematicalPhysicist]

Can you recommend me of books or preprints that cover reasonabely well this topic?

Thanks.

 

[quasar987]

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.

 

[MathematicalPhysicist]

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.

 

[gakushya]

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?

 

[mathwonk]

a similar question came up on mathoverflow.

http://mathoverflow.net/questions/80824/looking-for-a-book-on-banach-manifolds

 

[wisvuze]

Lang's "Fundamentals of Differential Geometry"

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