Topology From The Differentiable Viewpoint

Author : John Willard Milnor,David W. Weaver
Publisher : Princeton University Press
Page : 80 pages
File Size : 50,8 Mb
Release : 1997-12-14
Category : Mathematics
ISBN : 0691048339

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Topology from the Differentiable Viewpoint by John Willard Milnor,David W. Weaver Pdf

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.

Author : Morris W. Hirsch
Publisher : Springer Science & Business Media
Page : 230 pages
File Size : 44,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781468494495

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Differential Topology by Morris W. Hirsch Pdf

"A very valuable book. In little over 200 pages, it presents a well-organized and surprisingly comprehensive treatment of most of the basic material in differential topology, as far as is accessible without the methods of algebraic topology....There is an abundance of exercises, which supply many beautiful examples and much interesting additional information, and help the reader to become thoroughly familiar with the material of the main text." —MATHEMATICAL REVIEWS

Author : Victor Guillemin,Alan Pollack
Publisher : American Mathematical Soc.
Page : 242 pages
File Size : 46,7 Mb
Release : 2010
Category : Mathematics
ISBN : 9780821851937

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Differential Topology by Victor Guillemin,Alan Pollack Pdf

Differential Topology provides an elementary and intuitive introduction to the study of smooth manifolds. In the years since its first publication, Guillemin and Pollack's book has become a standard text on the subject. It is a jewel of mathematical exposition, judiciously picking exactly the right mixture of detail and generality to display the richness within. The text is mostly self-contained, requiring only undergraduate analysis and linear algebra. By relying on a unifying idea--transversality--the authors are able to avoid the use of big machinery or ad hoc techniques to establish the main results. In this way, they present intelligent treatments of important theorems, such as the Lefschetz fixed-point theorem, the Poincaré-Hopf index theorem, and Stokes theorem. The book has a wealth of exercises of various types. Some are routine explorations of the main material. In others, the students are guided step-by-step through proofs of fundamental results, such as the Jordan-Brouwer separation theorem. An exercise section in Chapter 4 leads the student through a construction of de Rham cohomology and a proof of its homotopy invariance. The book is suitable for either an introductory graduate course or an advanced undergraduate course.

Author : Tai-Danae Bradley,Tyler Bryson,John Terilla
Publisher : MIT Press
Page : 167 pages
File Size : 43,7 Mb
Release : 2020-08-18
Category : Mathematics
ISBN : 9780262359627

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Topology by Tai-Danae Bradley,Tyler Bryson,John Terilla Pdf

A graduate-level textbook that presents basic topology from the perspective of category theory. This graduate-level textbook on topology takes a unique approach: it reintroduces basic, point-set topology from a more modern, categorical perspective. Many graduate students are familiar with the ideas of point-set topology and they are ready to learn something new about them. Teaching the subject using category theory--a contemporary branch of mathematics that provides a way to represent abstract concepts--both deepens students' understanding of elementary topology and lays a solid foundation for future work in advanced topics.

Author : John McCleary
Publisher : Cambridge University Press
Page : 375 pages
File Size : 50,9 Mb
Release : 2013
Category : Mathematics
ISBN : 9780521116077

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Geometry from a Differentiable Viewpoint by John McCleary Pdf

A thoroughly revised second edition of a textbook for a first course in differential/modern geometry that introduces methods within a historical context.

Author : Raoul Bott,Loring W. Tu
Publisher : Springer Science & Business Media
Page : 319 pages
File Size : 55,5 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9781475739510

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Differential Forms in Algebraic Topology by Raoul Bott,Loring W. Tu Pdf

Developed from a first-year graduate course in algebraic topology, this text is an informal introduction to some of the main ideas of contemporary homotopy and cohomology theory. The materials are structured around four core areas: de Rham theory, the Cech-de Rham complex, spectral sequences, and characteristic classes. By using the de Rham theory of differential forms as a prototype of cohomology, the machineries of algebraic topology are made easier to assimilate. With its stress on concreteness, motivation, and readability, this book is equally suitable for self-study and as a one-semester course in topology.

Author : Theodor Bröcker,K. Jänich
Publisher : Cambridge University Press
Page : 176 pages
File Size : 49,5 Mb
Release : 1982-09-16
Category : Mathematics
ISBN : 0521284708

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Introduction to Differential Topology by Theodor Bröcker,K. Jänich Pdf

This book is intended as an elementary introduction to differential manifolds. The authors concentrate on the intuitive geometric aspects and explain not only the basic properties but also teach how to do the basic geometrical constructions. An integral part of the work are the many diagrams which illustrate the proofs. The text is liberally supplied with exercises and will be welcomed by students with some basic knowledge of analysis and topology.

Author : John M. Lee
Publisher : Springer Science & Business Media
Page : 395 pages
File Size : 49,6 Mb
Release : 2006-04-06
Category : Mathematics
ISBN : 9780387227276

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Introduction to Topological Manifolds by John M. Lee Pdf

Manifolds play an important role in topology, geometry, complex analysis, algebra, and classical mechanics. Learning manifolds differs from most other introductory mathematics in that the subject matter is often completely unfamiliar. This introduction guides readers by explaining the roles manifolds play in diverse branches of mathematics and physics. The book begins with the basics of general topology and gently moves to manifolds, the fundamental group, and covering spaces.

Author : John Milnor
Publisher : Princeton University Press
Page : 123 pages
File Size : 55,9 Mb
Release : 2015-12-08
Category : Mathematics
ISBN : 9781400878055

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Lectures on the H-Cobordism Theorem by John Milnor Pdf

These lectures provide students and specialists with preliminary and valuable information from university courses and seminars in mathematics. This set gives new proof of the h-cobordism theorem that is different from the original proof presented by S. Smale. Originally published in 1965. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Author : Osamu Saeki
Publisher : Springer Science & Business Media
Page : 164 pages
File Size : 47,5 Mb
Release : 2004
Category : Differentiable mappings
ISBN : 3540230211

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Topology of Singular Fibers of Differentiable Maps by Osamu Saeki Pdf

Author : Norbert A'Campo
Publisher : Springer Nature
Page : 282 pages
File Size : 50,6 Mb
Release : 2021-10-27
Category : Mathematics
ISBN : 9783030890322

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Topological, Differential and Conformal Geometry of Surfaces by Norbert A'Campo Pdf

This book provides an introduction to the main geometric structures that are carried by compact surfaces, with an emphasis on the classical theory of Riemann surfaces. It first covers the prerequisites, including the basics of differential forms, the Poincaré Lemma, the Morse Lemma, the classification of compact connected oriented surfaces, Stokes’ Theorem, fixed point theorems and rigidity theorems. There is also a novel presentation of planar hyperbolic geometry. Moving on to more advanced concepts, it covers topics such as Riemannian metrics, the isometric torsion-free connection on vector fields, the Ansatz of Koszul, the Gauss–Bonnet Theorem, and integrability. These concepts are then used for the study of Riemann surfaces. One of the focal points is the Uniformization Theorem for compact surfaces, an elementary proof of which is given via a property of the energy functional. Among numerous other results, there is also a proof of Chow’s Theorem on compact holomorphic submanifolds in complex projective spaces. Based on lecture courses given by the author, the book will be accessible to undergraduates and graduates interested in the analytic theory of Riemann surfaces.

Author : John M. Lee
Publisher : Springer Science & Business Media
Page : 646 pages
File Size : 40,6 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9780387217529

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Introduction to Smooth Manifolds by John M. Lee Pdf

Author has written several excellent Springer books.; This book is a sequel to Introduction to Topological Manifolds; Careful and illuminating explanations, excellent diagrams and exemplary motivation; Includes short preliminary sections before each section explaining what is ahead and why

Author : Anant R. Shastri
Publisher : CRC Press
Page : 319 pages
File Size : 53,6 Mb
Release : 2011-03-04
Category : Mathematics
ISBN : 9781439831632

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Elements of Differential Topology by Anant R. Shastri Pdf

Derived from the author's course on the subject, Elements of Differential Topology explores the vast and elegant theories in topology developed by Morse, Thom, Smale, Whitney, Milnor, and others. It begins with differential and integral calculus, leads you through the intricacies of manifold theory, and concludes with discussions on algebraic topol

Author : Anonim
Publisher : Unknown
Page : 64 pages
File Size : 43,6 Mb
Release : 1981
Category : Electronic
ISBN : OCLC:927617965

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Topology from the Differentiable Viewpoint by Anonim Pdf

Author : John Willard Milnor
Publisher : Princeton University Press
Page : 166 pages
File Size : 49,5 Mb
Release : 1963
Category : Mathematics
ISBN : 0691080089

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Morse Theory by John Willard Milnor Pdf

One of the most cited books in mathematics, John Milnor's exposition of Morse theory has been the most important book on the subject for more than forty years. Morse theory was developed in the 1920s by mathematician Marston Morse. (Morse was on the faculty of the Institute for Advanced Study, and Princeton published his Topological Methods in the Theory of Functions of a Complex Variable in the Annals of Mathematics Studies series in 1947.) One classical application of Morse theory includes the attempt to understand, with only limited information, the large-scale structure of an object. This kind of problem occurs in mathematical physics, dynamic systems, and mechanical engineering. Morse theory has received much attention in the last two decades as a result of a famous paper in which theoretical physicist Edward Witten relates Morse theory to quantum field theory. Milnor was awarded the Fields Medal (the mathematical equivalent of a Nobel Prize) in 1962 for his work in differential topology. He has since received the National Medal of Science (1967) and the Steele Prize from the American Mathematical Society twice (1982 and 2004) in recognition of his explanations of mathematical concepts across a wide range of scienti.c disciplines. The citation reads, "The phrase sublime elegance is rarely associated with mathematical exposition, but it applies to all of Milnor's writings. Reading his books, one is struck with the ease with which the subject is unfolding and it only becomes apparent after re.ection that this ease is the mark of a master.' Milnor has published five books with Princeton University Press.