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OverviewThis elegant book by distinguished mathematician John Milnor, provides a clear and succinct introduction to one of the most important subjects in modern mathematics. Beginning with basic concepts such as diffeomorphisms and smooth manifolds, he goes on to examine tangent spaces, oriented manifolds, and vector fields. Key concepts such as homotopy, the index number of a map, and the Pontryagin construction are discussed. The author presents proofs of Sard's theorem and the Hopf theorem. Full Product DetailsAuthor: John MilnorPublisher: Princeton University Press Imprint: Princeton University Press Edition: New edition Dimensions: Width: 15.20cm , Height: 0.70cm , Length: 22.90cm Weight: 0.113kg ISBN: 9780691048338ISBN 10: 0691048339 Pages: 80 Publication Date: 14 December 1997 Audience: Professional and scholarly , College/higher education , Professional & Vocational , Tertiary & Higher Education Format: Paperback Publisher's Status: Active Availability: Manufactured on demand  We will order this item for you from a manufactured on demand supplier. Language: English Table of ContentsPreface1Smooth manifolds and smooth maps1Tangent spaces and derivatives2Regular values7The fundamental theorem of algebra82The theorem of Sard and Brown10Manifolds with boundary12The Brouwer fixed point theorem133Proof of Sard's theorem164The degree modulo 2 of a mapping20Smooth homotopy and smooth isotopy205Oriented manifolds26The Brouwer degree276Vector fields and the Euler number327Framed cobordism; the Pontryagin construction42The Hopf theorem508Exercises52AppClassifying 1-manifolds55Bibliography59Index63ReviewsJohn Milnor, Winner of the 2011 Abel Prize from the Norwegian Academy of Science and Letters John Willard Milnor, Winner of the 2011 Leroy P. Steele Prize for Lifetime Achievement, American Mathematical Society John Willard Milnor, Winner of the 2011 Leroy P. Steele Prize for Lifetime Achievement, American Mathematical Society John Milnor, Winner of the 2011 Abel Prize from the Norwegian Academy of Science and Letters Author InformationTab Content 6Author Website:Countries AvailableAll regions |
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