Table of Contents
June 1, 2005 — Update May 12, 2009
No need to explain what is a table of contents. But, be aware that it can change with every new
Afterword
June 1, 2005 — Update June 14, 2008
A little bit of history about diffeology. If you have questions of suggestions to improve these
Solutions of the exercises
June 1, 2005 — Update May 12, 2009
(In progress) You shall find in this chapter the solutions of the exercises. All exercises did not
Chapter IX. Symplectic Diffeology
June 1, 2005 — Update May 15, 2009
First draft of the chapter about Symplectic Diffeology. This is more a program than a “complete”
Chapter VIII. Diffeological Fiber Bundles
June 1, 2005
(In progress) The chapter about diffeological Fiber Bundles is still not rewritten. Just parts of
Chapter VII. Diffeological Groups
June 1, 2005 — Update May 12, 2009
This is just the first draft of the chapter about diffeological groups. It can be improved until
Chapter VI. De Rham Calculus
June 1, 2005 — Update May 12, 2009
The chapter, about differential forms and De Rham calculus in diffeology, contains the basic
Chapter V. Homotopy of Diffeological Spaces
June 1, 2005 — Update May 12, 2009
(First draft) This Chapter introduces the basic constructions in homotopy for diffeological space.
Chapter IV. Modeling Spaces, Manifolds...
June 1, 2005 — Update May 12, 2009
The fourth chapter of the book is an introduction to manifolds. They are presented through the
Chapter III. Diffeological Vector Spaces
June 1, 2005 — Update May 12, 2009
The third chapter of the book is an introduction to diffeological vectors spaces. We don’t enter
Chapter II. Locality and Diffeologies
June 1, 2005 — Update May 12, 2009
In the second chapter we define the process of localization in diffeology. This chapter contains
Chapter I. Diffeology and Diffeological Spaces
June 1, 2005 — Update May 12, 2009
The first chapter presents the general framework of Diffeology. It contains the axiomatic, and the
Foreword
June 1, 2005 — Update June 14, 2008
The introduction and presentation of the book, in its present state. It will certainly still
The Draft
June 1, 2005 — Update May 12, 2009
This is the current Version of the DRAFT of the book. The chapters I, II, III, IV, V, VI, VII and
