# 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.