Kosinski has been Dovered

Some nice news -- Antoni Kosinski's Differential Manifolds book has been Dovered. The review on Amazon is pretty honest in that it's a book that's not without its problems. I don't know if it's me, but that just makes the book more readable. I've always had trouble reading Milnor's books because there aren't enough errors to keep me entertained. I like books to present the big idea, give me a few clues and then let me work out the details.

Kosinski's book has some typos and some weirdnesses. One weirdness that I found a bit `above and beyond' is that the book has a long and careful build-up to the h-cobordism theorem, but when it gets to the big magic Whitney trick moment, it defers to Milnor's h-cobordism notes... Milnor's notes for a long time had been out of print... which really annoyed me at the time. Luckily, those notes are readily found nowadays by anyone who can use a Google prompt. Alternatively, the Whitney trick can be learned from Whitney's papers.

Perhaps the thing that Kosinski's book does best is show how one can systematically avoid the dreaded `straightening the corners' problem that is inherent in Smale's h-cobordism proof. For that, it's worth a read.