Differential Topology

Differential Topology Author J. Margalef Roig
ISBN-10 9780444884343
Release 1992
Pages 603
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...there are reasons enough to warrant a coherent treatment of the main body of differential topology in the realm of Banach manifolds, which is at the same time correct and complete. This book fills the gap: whenever possible the manifolds treated are Banach manifolds with corners. Corners add to the complications and the authors have carefully fathomed the validity of all main results at corners. Even in finite dimensions some results at corners are more complete and better thought out here than elsewhere in the literature. The proofs are correct and with all details. I see this book as a reliable monograph of a well-defined subject; the possibility to fall back to it adds to the feeling of security when climbing in the more dangerous realms of infinite dimensional differential geometry. Peter W. Michor

Differential Topology

Differential Topology Author Victor Guillemin
ISBN-10 9780821851937
Release 2010
Pages 222
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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.

Introduction to Differential Topology

Introduction to Differential Topology Author T. Bröcker
ISBN-10 0521284708
Release 1982-09-16
Pages 160
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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.

Differential Topology

Differential Topology Author Andrew H. Wallace
ISBN-10 9780486150031
Release 2012-05-24
Pages 144
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DIVKeeping mathematical prerequisites to a minimum, this undergraduate-level text stimulates students' intuitive understanding of topology while avoiding the more difficult subtleties and technicalities. 1968 edition. /div

Differential Topology

Differential Topology Author Morris W. Hirsch
ISBN-10 9781468494495
Release 2012-12-06
Pages 222
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"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

Elementary Differential Topology AM 54

Elementary Differential Topology   AM 54 Author James R. Munkres
ISBN-10 9781400882656
Release 2016-03-02
Pages 112
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The description for this book, Elementary Differential Topology. (AM-54), Volume 54, will be forthcoming.

Differential Topology

Differential Topology Author David B. Gauld
ISBN-10 9780486319070
Release 2013-07-24
Pages 256
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Offering classroom-proven results, Differential Topology presents an introduction to point set topology via a naive version of nearness space. Its treatment encompasses a general study of surgery, laying a solid foundation for further study and greatly simplifying the classification of surfaces. This self-contained treatment features 88 helpful illustrations. Its subjects include topological spaces and properties, some advanced calculus, differentiable manifolds, orientability, submanifolds and an embedding theorem, and tangent spaces. Additional topics comprise vector fields and integral curves, surgery, classification of orientable surfaces, and Whitney's embedding theorem. Suitable for advanced undergraduate courses in introductory or differential topology, this volume also serves as a supplementary text in advanced calculus and physics courses, as well as a key source of information for students of mechanics.

Differential Topology

Differential Topology Author V. Villani
ISBN-10 3642111025
Release 2011-06-07
Pages 159
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A. Banyaga: On the group of diffeomorphisms preserving an exact symplectic.- G.A. Fredricks: Some remarks on Cauchy-Riemann structures.- A. Haefliger: Differentiable Cohomology.- J.N. Mather: On the homology of Haefliger’s classifying space.- P. Michor: Manifolds of differentiable maps.- V. Poenaru: Some remarks on low-dimensional topology and immersion theory.- F. Sergeraert: La classe de cobordisme des feuilletages de Reeb de S3 est nulle.- G. Wallet: Invariant de Godbillon-Vey et difféomorphismes commutants.

Collected Papers of John Milnor

Collected Papers of John Milnor Author John Willard Milnor
ISBN-10 9780821842300
Release 2007
Pages 343
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The field of differential topology underwent a dramatic development period between 1955 and 1965. This collection of articles written by one of the creators of this field contains not only original papers, but also previously unpublished expository lectures. It includes commentary by the author, filling in some of the historical context, and outlining subsequent developments. It includes a rich bibliography of newer and older papers, providing a wider and deeper understanding of the subject. It also outlines the actual state of the art, and provides an index that will allow the reader to browse easily through the book. Of particular interest are the articles related to the existence of exotic differentiable structures on spheres, the achievement for which J. Milnor was awarded the Fields Medal in 1962.

Techniques of Differential Topology in Relativity

Techniques of Differential Topology in Relativity Author Roger Penrose
ISBN-10 9780898710052
Release 1972-06-01
Pages 72
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Acquaints the specialist in relativity theory with some global techniques for the treatment of space-times and will provide the pure mathematician with a way into the subject of general relativity.

Differential Topology

Differential Topology Author Amiya Mukherjee
ISBN-10 9783319190457
Release 2015-06-30
Pages 349
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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.

A History of Algebraic and Differential Topology 1900 1960

A History of Algebraic and Differential Topology  1900   1960 Author Jean Dieudonné
ISBN-10 0817649077
Release 2009-09-01
Pages 648
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This book is a well-informed and detailed analysis of the problems and development of algebraic topology, from Poincaré and Brouwer to Serre, Adams, and Thom. The author has examined each significant paper along this route and describes the steps and strategy of its proofs and its relation to other work. Previously, the history of the many technical developments of 20th-century mathematics had seemed to present insuperable obstacles to scholarship. This book demonstrates in the case of topology how these obstacles can be overcome, with enlightening results.... Within its chosen boundaries the coverage of this book is superb. Read it! —MathSciNet

Differential topology with a view to applications

Differential topology with a view to applications Author David Chillingworth
ISBN-10 027300283X
Release 1976
Pages 291
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Differential topology with a view to applications has been writing in one form or another for most of life. You can find so many inspiration from Differential topology with a view to applications also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Differential topology with a view to applications book for free.

Critical Point Theory in Global Analysis and Differential Topology

Critical Point Theory in Global Analysis and Differential Topology Author
ISBN-10 0080873456
Release 2014-05-14
Pages 388
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Critical Point Theory in Global Analysis and Differential Topology

Differential Topology

Differential Topology Author C. T. C. Wall
ISBN-10 9781107153523
Release 2016-07-04
Pages 353
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Exploring the full scope of differential topology, this comprehensive account of geometric techniques for studying the topology of smooth manifolds offers a wide perspective on the field. Building up from first principles, concepts of manifolds are introduced, supplemented by thorough appendices giving background on topology and homotopy theory. Deep results are then developed from these foundations through in-depth treatments of the notions of general position and transversality, proper actions of Lie groups, handles (up to the h-cobordism theorem), immersions and embeddings, concluding with the surgery procedure and cobordism theory. Fully illustrated and rigorous in its approach, little prior knowledge is assumed, and yet growing complexity is instilled throughout. This structure gives advanced students and researchers an accessible route into the wide-ranging field of differential topology.

Elements of Differential Topology

Elements of Differential Topology Author Anant R. Shastri
ISBN-10 9781439831632
Release 2011-03-04
Pages 319
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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 topology, algebraic/differential geometry, and Lie groups. The first two chapters review differential and integral calculus of several variables and present fundamental results that are used throughout the text. The next few chapters focus on smooth manifolds as submanifolds in a Euclidean space, the algebraic machinery of differential forms necessary for studying integration on manifolds, abstract smooth manifolds, and the foundation for homotopical aspects of manifolds. The author then discusses a central theme of the book: intersection theory. He also covers Morse functions and the basics of Lie groups, which provide a rich source of examples of manifolds. Exercises are included in each chapter, with solutions and hints at the back of the book. A sound introduction to the theory of smooth manifolds, this text ensures a smooth transition from calculus-level mathematical maturity to the level required to understand abstract manifolds and topology. It contains all standard results, such as Whitney embedding theorems and the Borsuk–Ulam theorem, as well as several equivalent definitions of the Euler characteristic.

Differential Topology

Differential Topology Author Ulrich Koschorke
ISBN-10 STANFORD:36105032437985
Release 1988
Pages 269
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It is surprising how little is actually known about the fate of wastewater bacteria once they enter the sea. This wide-ranging work is one of the first to unravel the mechanisms determining bacterial sensitivity or survival under these conditions.