By Antoni A. Kosinski
"How worthy it is," famous the Bulletin of the yank Mathematical Society, "to have a unmarried, brief, well-written ebook on differential topology." This quantity starts off with a close, self-contained overview of the rules of differential topology that calls for just a minimum wisdom of basic algebraic topology. next chapters clarify the means of becoming a member of manifolds alongside submanifolds, the deal with presentation theorem, and the facts of the h-cobordism theorem in line with those structures. There follows a bankruptcy at the Pontriagin Construction—the crucial hyperlink among differential topology and homotopy concept. the ultimate bankruptcy introduces the tactic of surgical procedure and applies it to the class of delicate constructions of spheres. The textual content is supplemented through quite a few fascinating old notes and includes a new appendix, "The paintings of Grigory Perelman," by means of John W. Morgan, which discusses the latest advancements in differential topology.
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Differential Manifolds (Dover Books on Mathematics) by Antoni A. Kosinski