Topology from the Differentiable Viewpoint

"John Willard Milnor, Winner of the 2011 Leroy P. Steele Prize for Lifetime Achievement, American Mathematical Society" Informationen zum Autor John Milnor Klappentext This 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. Zusammenfassung Provides a clear introduction to one of the important subjects in modern mathematics. Beginning with basic concepts such as diffeomorphisms and smooth manifolds, this book goes on to examine tangent spaces, oriented manifolds, and vector fields. It discusses concepts such as homotopy, the index number of a map, and the Pontryagin construction. Inhaltsverzeichnis Preface1Smooth 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-manifolds55Bibliography59Index63

Product details

• Authors: John Milnor, John W. Milnor, John Willard Milnor
• Publisher: Princeton University Press
• Languages: English
• Product format: Paperback / Softback
• Released: 18.07.2002
• EAN: 9780691048338
• ISBN: 978-0-691-04833-8
• No. of pages: 64
• Dimensions: 150 mm x 228 mm x 8 mm
• Series: Princeton Landmarks in Mathematics and Physics; Princeton Landmarks in Mathematics and Physics; Princeton Landmarks in Mathema
• Subjects: Education and learning > Teaching preparation > Vocational needs; Natural sciences, medicine, IT, technology > Mathematics > Miscellaneous; MATHEMATICS / Geometry / General, MATHEMATICS / Topology, geometry, Topology