Differential Manifolds (Dover Books on Mathematics) - download pdf or read online

By Antoni A. Kosinski

ISBN-10: 0124218504

ISBN-13: 9780124218505

ISBN-10: 0486462447

ISBN-13: 9780486462448

The recommendations of differential topology shape the guts of many mathematical disciplines resembling differential geometry and Lie crew thought. Differential Manifolds offers to complex undergraduates and graduate scholars the systematic research of the topological constitution of delicate manifolds. writer Antoni A. Kosinski, Professor Emeritus of arithmetic at Rutgers college, deals an available method of either the h-cobordism theorem and the class of differential buildings on spheres.
"How important it is," famous the Bulletin of the yankee Mathematical Society, "to have a unmarried, brief, well-written publication on differential topology." This quantity starts off with a close, self-contained evaluation of the principles of differential topology that calls for just a minimum wisdom of undemanding algebraic topology. next chapters clarify the means of becoming a member of manifolds alongside submanifolds, the deal with presentation theorem, and the evidence of the h-cobordism theorem in keeping with those structures. There follows a bankruptcy at the Pontriagin Construction—the primary hyperlink among differential topology and homotopy concept. the ultimate bankruptcy introduces the tactic of surgical procedure and applies it to the class of gentle constructions of spheres. The textual content is supplemented via quite a few attention-grabbing old notes and incorporates a new appendix, "The paintings of Grigory Perelman," via John W. Morgan, which discusses the newest advancements in differential topology.

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