The following books and/or notes develop various aspects of the theory of infinite-dimensional manifolds:

  1. Lang, Fundamentals of Differential Geometry.
  2. Kriegl & Michor, The Convenient Setting of Global Analysis.
  3. Choquet-Bruhat & DeWitt-Morette, Analysis, Manifolds and Physics.
  4. Klingenberg, Riemannian Geometry.
  5. Marsden, Ratiu, and Abraham, Manifolds, Tensor Analysis, and Applications.
  6. Hamilton, The inverse function theorem of Nash and Moser.

Question: Are there any other books that systematically develop from scratch the theory of infinite-dimensional manifolds, in particular Frechet manifolds?


2 Answers 2


It's not specifically a text on infinite-dimensional manifolds, but the theory of diffeology developed in Patrick Iglesias-Zemmour's text encompasses infinite dimensional manifolds of all sorts (Banach, Frechet, etc.). The category of diffeological spaces is also a quasi-topos, which is a really fantastic property.


Infinite-Dimensional Lie Groups by Karl-Hermann Neeb looks really nice. It includes basics of the theory of infinite-dimensional manifolds in chapter 2. He also shows how the theory of linear ODEs collapses for Frechet spaces.


You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .