# nLab Banach manifold

### Context

#### Differential geometry

differential geometry

synthetic differential geometry

## Applications

#### Manifolds and cobordisms

manifolds and cobordisms

# 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). For more see at Fréchet manifold – Relation to diffeological spaces.

## 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)

Revised on March 6, 2015 07:40:50 by Urs Schreiber (195.113.30.252)