I am almost finished with a book, an advanced
introduction to differential manifolds, bundles, and groups, that began as
the lecture notes for my 2011--13 seminars. There is also an appendix that
may be integrated into the book, Manifolds in Fluid
Dynamics by J. Ryan. In addition to the exercises in my book,
there are also some good ones in Bröcker &
Jänich and in Warner, even though some of
his notation is archaic, to put it kindly.
The category theory needed is almost covered by 713 as I have taught it.
One additional result is used exactly twice: that right adjoints preserve
products, found in MacLane's
Remarks and comments, however, may assume much more: homotopy,
(co)homology, nuclear HLCTVSs, topological function spaces,
Indeed, I am looking for someone to assist me in developing analysis on complete, nuclear k-spaces, using that on Fréchet spaces in particular and on Hausdorff locally convex TVSs in general as a model and/or guide. It should make a good MS thesis at least. If you might be interested, let me know. |