nLab
convenient manifold

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Context

Differential geometry

differential geometry

synthetic differential geometry

Axiomatics

Models

Concepts

Theorems

Applications

Manifolds and cobordisms

manifolds and cobordisms

Definitions

Genera and invariants

Theorem

Contents

Idea

A manifold, possibly infinite-dimensional, is called a convenient manifold – implicitly meaning: convenient for differential geometry – if it is modeled on a convenient vector space.

One should note that this usage of the adjective ‘convenient’ is different to that in ‘convenient category’, for example of smooth spaces. In that case the category is convenient, whereas here the objects are convenient.

Properties

Embedding into the Cahiers-topos

Together with convenient vector spaces, convenient manifods embed into the Cahier topos? of synthetic differential smooth spaces. See at Cahiers topos for more on this.

References

A standard textbook reference is

  • Peter Michor, A convenient setting for differential geometry and global analysis, Cahiers Topologie Géom. Différentielle 25 (1984), no. 1, 63–109, MR86g:58014a; A convenient setting for differential geometry and global analysis. II, Cahiers Topologie Géom. Différentielle 25 (1984), no. 2, 113–178.

A survey is for instance in the slides

  • Richard Blute, Convenient Vector Spaces, Convenient Manifolds and Differential Linear Logic (2011) (pdf)
  • John C. Baez, Alexander E. Hoffnung, Convenient categories of smooth spaces, Trans. Amer. Math. Soc. 363 (2011), 5789-5825 pdf

Revised on February 9, 2013 22:24:07 by Urs Schreiber (82.113.98.230)
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