December 14, 2012 — Sent back the revisions of the Galley proofs. The book is in the hands of the AMS now, under press and must be on the shelves in March 2013.
November 19, 2012 — Received the Galley proofs. Jennifer Wright Sharp from AMS has made a wonderful editor job, fixing all the mistakes remained in the manuscript. Thanks Jennifer!
August 8, 2012 — The first final version of the book is finished and sent to the editor. The next changes will be in the Galley proofs.
July 18, 2012 — Finished the solutions of the exercises. Still to do : language revisions, format for AMS Survey.
May/June/July, 2012 — Fixing text, preparing for publication.
November 30, 2011 — Fixed a mistake in last question of exercise “The powerset diffeology of the set of lines”.
July 20, 2011 — Correction of exercises, continued...
July 12, 2011 — Rewrote “Section of a quotient”, and correction of exercises...
July 4, 2011 — Adding corrections of the exercises.
July 1st, 2011 — I think I finished the introduction.
June 28, 2011 — Added a few citations, improved the introduction.
June 26, 2011 — Finished the last paragraph of chapter VIII, on the characteristic bundle of a closed 2-form. The chaper VIII is thus finished too, and therefore the book itself :-) Well, not really completely. I have to finish to write down the corrections of the exercises, but this is not the same kind of work. The exercises may still change. And then, I have to read again the whole book, fix the last mistakes and misprints. It may take stil one or two months. Stay tuned...
June 22, 2011 — Wrote paragraph on torus bundles over diffeological spaces. Still two paragraphs to write on this last chapter...
June 7, 2011 — Wrote paragraph on R-bundles over irrational tori and small divisors.
June 2, 2011 — Wrote the paragraph on irrational torus and fibrations.
May 25, 2011 — Restructured the integration of closed 1 and 2 forms in part VIII. Modified some things here and there. Decided to rewrite the chapter on integration of closed 2-form. Still not satisfied with the outcome, stay tuned !
April 10, 2011 — After having been busy somewhere, I come back to the book. I fixed an exercise on 1-forms vanishing on loops in chapter 6. I modify a definition of the group of periods of closed 1 and 2 forms, fixed a mistake in the previous version. I’m trying no to fix the paragraph on integration of closed 2-form but it takes time.
February 13, 2011 — Added an exercise and correction on the homogeneity of manifolds.
January 19, 2011 — Improved integration bundle of a closed 2-form paragraph.
January 12, 2011 — Cleaned up the section about connections, made some progress to finish the section about integration of a closed 2-form.
January 9, 2011 — Finished (I think) the paragraph on characterisc fiber bundle of a closed 2-form, and cleaned up the part on solutions of exercises.
December 30, 2010 — Replaced “open superset” by “open neighborood”, after some advice I came back to a more classical wording.
December 26, 2010 — Replaced “superset” by “open superset” everywhere it could lead confusion, prefering redundancy to doubt .
December 24, 2010 — Added a paragraph to the Foreword and made some modifications.
December 9, 2010 — Rewrote the paragraph 1.42 on Klein structure and singularities. Was not clear enough.
June 20, 2010 — Done with chapter on coverings. It may still change but not much.
June 19, 2010 — Done with paragraph on universal covering.
June 18, 2010 — Finished paragraph on Covering and fundamental group, and paragraph about monodromy theorem, in chapter VIII. Added the back cover to the book with a first try of a summary.
June 16, 2010 — Fixed various typos in chapters 1 to V, they must be free of typos now ? If you find some typo just send me an e-mail. And also, put the new versions of the chapters on the site.
June 15, 2010 — Wrote again the paragraph on characteristic bundles of closed 2-forms in chapter VIII and proof.
June 11, 2010 — Added paragraph on characteristic bundles of closed 2-forms in chapter VIII. It is still not finished but readable. I’ll write it as a separated self-contained paper soon.
June 4, 2010 — Decided to remove the paragraph on characteristic bundles of closed 2-forms in chapter VIII until it get its final form and everything is checked.
June 3, 2010 — Continued to write the paragraph on characteristic bundles of closed 2-forms in chapter VIII. The proof of the main theorem is still not written down, so the statelent may change slightly. Must be true but be careful, wait next edition.
June 1, 2010 — Fixed a mistake in an exercise about deformation paths onto stationnary paths, the spaces Paths(X) and stPaths(X) are homotopic equivalent. Moved the paragraph on integration bundles of closed 1-forms into the chapter Fiber Bundles, and began the paragraph integration bundles of closed 2-forms which contains a new result about the general construction of every diffeological space as a direct quotient of the space of paths.
May 30, 2010 — Continuing paragraph on coverings of diffeological spaces and made some cosmetic changes. I have a class on characteristic classes to prepare, no much time to improve the manuscript today.
May 28, 2010 — Began the paragraph on coverings of diffeological spaces.
May 27, 2010 — Rewrote the paragraph on extensions of group (here), and finished a redaction of the proof on the exact homotopy sequence of a diffeological fiber bundle.
May 26, 2010 — Rewrote some parts of the Homotopy chapter: Wrote the paragraph on the exact homotopy sequence of a diffeological fiber bundle, the proof will come.
May 24, 2010 — Wrote down a missing paragraph: Associated loops fiber bundles. Need to come back and clean up the proof, still too messy.
May 22, 2010 — Finished paragraph on Space of Structures of a Fiber Bundle, made some change to previous paragraphs. Beginning paragraph on Exact Homotopy Sequence of Fiber Bundles.
May 20, 2010 — Rewrote paragraph on principal fiber bundles and finished paragraph on structured bundles.
May 18, 2010 — Finishing Structured Fiber Bundles paragraph.
May 16, 2010 — Cosmetic changes.
May 14, 2010 — Added exercise on wired diffeology and differental form. Added a note about retraction compatible with subduction.
April 23, 2010 — Rewrote “Compact controlled diffeology” in chapter I.
April 21, 2010 — Added exercise “Playing with SO(3)” in the fiber bundle chapter to illustrate principal and associated fiber bundles. Corrected various misprints.
April 19, 2010 — Change the exercise “A discrete image of R”. Change exercise “Compact diffeology”, and fix a mistake in the solution. Added note to “Differential forms are local”. Added a paragrah “Compact controlled functional diffeology” to chapter I, Functional Diffeology. Some vocabulary fixes (powerset diffeology instead of power-diffeology, aso). Continued paragraph "Structures on fiber bundles".
April 14, 2010 — Fix misprints in proof of "Associated fiber bundles. Beginning paragraph "Structures on fiber bundles".
The Diffeology Book 
Last Updates
This is the list of modifications of the Diffeology book along its writting. The book is finished now and close to be distributed by the AMS. If you still find a mistakes or a misprint send me a mail, I’will put an erratum in the Diffeology blog, there...The%20Book.html