Lectures On Differential Topology
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Lectures On Differential Topology
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Author : Riccardo Benedetti
language : en
Publisher:
Release Date : 1900
Lectures On Differential Topology written by Riccardo Benedetti and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1900 with Differential topology categories.
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 number.
Lectures On Differential Topology
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Author : Riccardo Benedetti
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-10-27
Lectures On Differential Topology written by Riccardo Benedetti and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-27 with Education categories.
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 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. This book will be useful as a textbook for beginning masters and doctoral students interested in differential topology, who have finished a standard undergraduate mathematics curriculum. It emphasizes an active learning approach, and exercises are included within the text as part of the flow of ideas. Experienced readers may use this book as a source of alternative, constructive approaches to results commonly presented in more advanced contexts with specialized techniques.
Lectures On Algebraic And Differential Topology
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Author : R. Bott
language : en
Publisher: Springer
Release Date : 2006-11-15
Lectures On Algebraic And Differential Topology written by R. Bott and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
Lectures On The Differential Topology Of Infinite Dimensional Manifolds
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Author : Richard S. Palais
language : en
Publisher:
Release Date : 1965
Lectures On The Differential Topology Of Infinite Dimensional Manifolds written by Richard S. Palais and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1965 with Differential topology categories.
Lectures On Algebraic And Differential Topology
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Author : Raoul Bott
language : en
Publisher:
Release Date : 1972
Lectures On Algebraic And Differential Topology written by Raoul Bott and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972 with Algebraic topology categories.
Lectures On Differential Geometry
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Author : Shlomo Sternberg
language : en
Publisher: Chelsea Publishing Company, Incorporated
Release Date : 1983
Lectures On Differential Geometry written by Shlomo Sternberg and has been published by Chelsea Publishing Company, Incorporated this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with Mathematics categories.
Lectures On Differential Geometry
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Author : Richard M. Schoen
language : en
Publisher:
Release Date : 1994
Lectures On Differential Geometry written by Richard M. Schoen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Geometry, Differential categories.
Lectures On The Geometry Of Manifolds
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Author : Liviu I. Nicolaescu
language : en
Publisher: World Scientific
Release Date : 2007
Lectures On The Geometry Of Manifolds written by Liviu I. Nicolaescu and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
The goal of this book is to introduce the reader to some of the most frequently used techniques in modern global geometry. Suited to the beginning graduate student willing to specialize in this very challenging field, the necessary prerequisite is a good knowledge of several variables calculus, linear algebra and point-set topology.The book's guiding philosophy is, in the words of Newton, that ?in learning the sciences examples are of more use than precepts?. We support all the new concepts by examples and, whenever possible, we tried to present several facets of the same issue.While we present most of the local aspects of classical differential geometry, the book has a ?global and analytical bias?. We develop many algebraic-topological techniques in the special context of smooth manifolds such as Poincar duality, Thom isomorphism, intersection theory, characteristic classes and the Gauss-;Bonnet theorem.We devoted quite a substantial part of the book to describing the analytic techniques which have played an increasingly important role during the past decades. Thus, the last part of the book discusses elliptic equations, including elliptic Lpand Hlder estimates, Fredholm theory, spectral theory, Hodge theory, and applications of these. The last chapter is an in-depth investigation of a very special, but fundamental class of elliptic operators, namely, the Dirac type operators.The second edition has many new examples and exercises, and an entirely new chapter on classical integral geometry where we describe some mathematical gems which, undeservedly, seem to have disappeared from the contemporary mathematical limelight.
Differential Topology
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Author : Amiya Mukherjee
language : en
Publisher: Birkhäuser
Release Date : 2015-06-30
Differential Topology written by Amiya Mukherjee and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-06-30 with Mathematics categories.
This book presents a systematic and comprehensive account of the theory of differentiable manifolds and provides the necessary background for the use of fundamental differential topology tools. The text includes, in particular, the earlier works of Stephen Smale, for which he was awarded the Fields Medal. Explicitly, the topics covered are Thom transversality, Morse theory, theory of handle presentation, h-cobordism theorem and the generalised Poincaré conjecture. The material is the outcome of lectures and seminars on various aspects of differentiable manifolds and differential topology given over the years at the Indian Statistical Institute in Calcutta, and at other universities throughout India. The book will appeal to graduate students and researchers interested in these topics. An elementary knowledge of linear algebra, general topology, multivariate calculus, analysis and algebraic topology is recommended.
Elementary Differential Topology
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Author : James R. Munkres
language : en
Publisher:
Release Date : 1963
Elementary Differential Topology written by James R. Munkres and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1963 with Differential topology categories.