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Author : James R. Munkres
Publisher : Princeton University Press
Page : 112 pages
File Size : 46,6 Mb
Release : 2016-03-02
Category : Mathematics
ISBN : 9781400882656
The description for this book, Elementary Differential Topology. (AM-54), Volume 54, will be forthcoming.
Author : James R. Munkres
Publisher : Princeton University Press
Page : 136 pages
File Size : 45,6 Mb
Release : 1966
Category : Mathematics
ISBN : 0691090939
Annotation The Description for this book, Elementary Differential Topology. (AM-54), will be forthcoming.
Author : Victor Guillemin,Alan Pollack
Publisher : American Mathematical Soc.
Page : 242 pages
File Size : 46,9 Mb
Release : 2010
Category : Mathematics
ISBN : 9780821851937
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 : Anant R. Shastri
Publisher : CRC Press
Page : 319 pages
File Size : 42,6 Mb
Release : 2011-03-04
Category : Mathematics
ISBN : 9781439831632
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 : Theodor Bröcker,K. Jänich
Publisher : Cambridge University Press
Page : 176 pages
File Size : 45,6 Mb
Release : 1982-09-16
Category : Mathematics
ISBN : 0521284708
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 : Amiya Mukherjee
Publisher : Birkhäuser
Page : 349 pages
File Size : 46,7 Mb
Release : 2015-06-30
Category : Mathematics
ISBN : 9783319190457
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.
Author : John Willard Milnor,David W. Weaver
Publisher : Princeton University Press
Page : 80 pages
File Size : 50,9 Mb
Release : 1997-12-14
Category : Mathematics
ISBN : 0691048339
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 : 43,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781468494495
"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 : Anonim
Publisher : Unknown
Page : 112 pages
File Size : 45,8 Mb
Release : 1966
Category : Electronic
ISBN : OCLC:911963622
Author : Viktor Vasilʹevich Prasolov
Publisher : American Mathematical Soc.
Page : 432 pages
File Size : 49,5 Mb
Release : 2007
Category : Mathematics
ISBN : 9780821838129
The book is a continuation of the previous book by the author (Elements of Combinatorial and Differential Topology, Graduate Studies in Mathematics, Volume 74, American Mathematical Society, 2006). It starts with the definition of simplicial homology and cohomology, with many examples and applications. Then the Kolmogorov-Alexander multiplication in cohomology is introduced. A significant part of the book is devoted to applications of simplicial homology and cohomology to obstruction theory, in particular, to characteristic classes of vector bundles. The later chapters are concerned with singular homology and cohomology, and Cech and de Rham cohomology. The book ends with various applications of homology to the topology of manifolds, some of which might be of interest to experts in the area. The book contains many problems; almost all of them are provided with hints or complete solutions.
Author : J. Margalef-Roig,E. Outerelo Dominguez
Publisher : Elsevier
Page : 602 pages
File Size : 53,7 Mb
Release : 1992-06-02
Category : Mathematics
ISBN : 9780080872841
...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
Author : Andrew H. Wallace
Publisher : Courier Corporation
Page : 149 pages
File Size : 42,8 Mb
Release : 2012-05-24
Category : Mathematics
ISBN : 9780486150031
Keeping mathematical prerequisites to a minimum, this undergraduate-level text stimulates students' intuitive understanding of topology while avoiding the more difficult subtleties and technicalities. Its focus is the method of spherical modifications and the study of critical points of functions on manifolds. No previous knowledge of topology is necessary for this text, which offers introductory material regarding open and closed sets and continuous maps in the first chapter. Succeeding chapters discuss the notions of differentiable manifolds and maps and explore one of the central topics of differential topology, the theory of critical points of functions on a differentiable manifold. Additional topics include an investigation of level manifolds corresponding to a given function and the concept of spherical modifications. The text concludes with applications of previously discussed material to the classification problem of surfaces and guidance, along with suggestions for further reading and study.
Author : James R. Munkres
Publisher : Unknown
Page : 130 pages
File Size : 54,6 Mb
Release : 1963
Category : Differential topology
ISBN : STANFORD:36105032176070
Author : I.M. Singer,J.A. Thorpe
Publisher : Springer
Page : 240 pages
File Size : 53,9 Mb
Release : 2015-05-28
Category : Mathematics
ISBN : 9781461573470
At the present time, the average undergraduate mathematics major finds mathematics heavily compartmentalized. After the calculus, he takes a course in analysis and a course in algebra. Depending upon his interests (or those of his department), he takes courses in special topics. Ifhe is exposed to topology, it is usually straightforward point set topology; if he is exposed to geom etry, it is usually classical differential geometry. The exciting revelations that there is some unity in mathematics, that fields overlap, that techniques of one field have applications in another, are denied the undergraduate. He must wait until he is well into graduate work to see interconnections, presumably because earlier he doesn't know enough. These notes are an attempt to break up this compartmentalization, at least in topology-geometry. What the student has learned in algebra and advanced calculus are used to prove some fairly deep results relating geometry, topol ogy, and group theory. (De Rham's theorem, the Gauss-Bonnet theorem for surfaces, the functorial relation of fundamental group to covering space, and surfaces of constant curvature as homogeneous spaces are the most note worthy examples.) In the first two chapters the bare essentials of elementary point set topology are set forth with some hint ofthe subject's application to functional analysis.
Author : Christian Bär
Publisher : Cambridge University Press
Page : 335 pages
File Size : 53,5 Mb
Release : 2010-05-06
Category : Mathematics
ISBN : 9780521896719
This easy-to-read introduction takes the reader from elementary problems through to current research. Ideal for courses and self-study.