Read Lectures on Differential Topology (Graduate Studies in Mathematics, 218)

Lectures on Differential Topology (Graduate Studies in Mathematics, 218)

Riccardo Benedetti

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Description:This book gives a comprehensive introduction to the theory of smooth manifolds, maps, and fundamental associated structures with an emphasis on “bare hands” approaches, combining differential-topological cut-and-paste procedures and applications of transversality. In particular, the smooth cobordism cup-product is defined from scratch and used as the main tool in a variety of settings. After establishing the fundamentals, the book proceeds to a broad range of more advanced topics in differential topology, including degree theory, the Poincaré-Hopf index theorem, bordism-characteristic numbers, and the Pontryagin-Thom construction. Cobordism intersection forms are used to classify compact surfaces; their quadratic enhancements are developed and applied to studying the homotopy groups of spheres, the bordism group of immersed surfaces in a 3-manifold, and congruences mod 16 for the signature of intersection forms of 4-manifolds. Other topics include the high-dimensional h-cobordism theorem stressing the role of the “Whitney trick”, a determination of the singleton bordism modules in low dimensions, and proofs of parallelizability of orientable 3-manifolds and the Lickorish-Wallace theorem. Nash manifolds and Nash's questions on the existence of real algebraic models are also discussed.We have made it easy for you to find a PDF Ebooks without any digging. And by having access to our ebooks online or by storing it on your computer, you have convenient answers with Lectures on Differential Topology (Graduate Studies in Mathematics, 218). To get started finding Lectures on Differential Topology (Graduate Studies in Mathematics, 218), you are right to find our website which has a comprehensive collection of manuals listed.
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ISBN: 1470462710

Description: This book gives a comprehensive introduction to the theory of smooth manifolds, maps, and fundamental associated structures with an emphasis on “bare hands” approaches, combining differential-topological cut-and-paste procedures and applications of transversality. In particular, the smooth cobordism cup-product is defined from scratch and used as the main tool in a variety of settings. After establishing the fundamentals, the book proceeds to a broad range of more advanced topics in differential topology, including degree theory, the Poincaré-Hopf index theorem, bordism-characteristic numbers, and the Pontryagin-Thom construction. Cobordism intersection forms are used to classify compact surfaces; their quadratic enhancements are developed and applied to studying the homotopy groups of spheres, the bordism group of immersed surfaces in a 3-manifold, and congruences mod 16 for the signature of intersection forms of 4-manifolds. Other topics include the high-dimensional h-cobordism theorem stressing the role of the “Whitney trick”, a determination of the singleton bordism modules in low dimensions, and proofs of parallelizability of orientable 3-manifolds and the Lickorish-Wallace theorem. Nash manifolds and Nash's questions on the existence of real algebraic models are also discussed.We have made it easy for you to find a PDF Ebooks without any digging. And by having access to our ebooks online or by storing it on your computer, you have convenient answers with Lectures on Differential Topology (Graduate Studies in Mathematics, 218). To get started finding Lectures on Differential Topology (Graduate Studies in Mathematics, 218), you are right to find our website which has a comprehensive collection of manuals listed.
Our library is the biggest of these that have literally hundreds of thousands of different products represented.

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Lectures on Differential Topology (Graduate Studies in Mathematics, 218)

Lectures on Differential Topology (Graduate Studies in Mathematics, 218)

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