nLab
Banach manifold

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Context

Differential geometry

differential geometry

synthetic differential geometry

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Manifolds and cobordisms

manifolds and cobordisms

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Contents

Idea

A notion of infinite-dimensional manifold. A Banach manifold is a manifold modelled on Banach spaces. By default, transition maps are taken to be smooth.

Properties

Embedding into the category of diffeological spaces

The category of smooth Banach manifolds has a full and faithful functor into the category of diffeological spaces. In terms of Chen smooth spaces this was observed in (Hain), a discussion for genuine diffeological spaces is in the textbook (Iglesias-Zemmour, exercise 72).

References

For general references see at infinite-dimensional manifold.

The embedding into the category of diffeological spaces is discussed in

  • Richard Hain, A characterization of smooth functions defined on a Banach space, Proc. Amer. Math. Soc. 77 (1979), 63-67 (web, pdf)

More on this is in exercise 72 of

Revised on March 13, 2013 11:44:33 by Urs Schreiber (82.169.65.155)
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