differential topology ams chelsea publishing

Download Book Differential Topology Ams Chelsea Publishing in PDF format. You can Read Online Differential Topology Ams Chelsea Publishing here in PDF, EPUB, Mobi or Docx formats.

Differential Topology

Author : Victor Guillemin
ISBN : 9780821851937
Genre : Mathematics
File Size : 48. 71 MB
Format : PDF
Download : 881
Read : 397

Get This Book


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.

Differentialgeometrie Topologie Und Physik

Author : Mikio Nakahara
ISBN : 9783662453001
Genre : Science
File Size : 31. 46 MB
Format : PDF, Kindle
Download : 953
Read : 642

Get This Book


Differentialgeometrie und Topologie sind wichtige Werkzeuge für die Theoretische Physik. Insbesondere finden sie Anwendung in den Gebieten der Astrophysik, der Teilchen- und Festkörperphysik. Das vorliegende beliebte Buch, das nun erstmals ins Deutsche übersetzt wurde, ist eine ideale Einführung für Masterstudenten und Forscher im Bereich der theoretischen und mathematischen Physik. - Im ersten Kapitel bietet das Buch einen Überblick über die Pfadintegralmethode und Eichtheorien. - Kapitel 2 beschäftigt sich mit den mathematischen Grundlagen von Abbildungen, Vektorräumen und der Topologie. - Die folgenden Kapitel beschäftigen sich mit fortgeschritteneren Konzepten der Geometrie und Topologie und diskutieren auch deren Anwendungen im Bereich der Flüssigkristalle, bei suprafluidem Helium, in der ART und der bosonischen Stringtheorie. - Daran anschließend findet eine Zusammenführung von Geometrie und Topologie statt: es geht um Faserbündel, characteristische Klassen und Indextheoreme (u.a. in Anwendung auf die supersymmetrische Quantenmechanik). - Die letzten beiden Kapitel widmen sich der spannendsten Anwendung von Geometrie und Topologie in der modernen Physik, nämlich den Eichfeldtheorien und der Analyse der Polakov'schen bosonischen Stringtheorie aus einer gemetrischen Perspektive. Mikio Nakahara studierte an der Universität Kyoto und am King’s in London Physik sowie klassische und Quantengravitationstheorie. Heute ist er Physikprofessor an der Kinki-Universität in Osaka (Japan), wo er u. a. über topologische Quantencomputer forscht. Diese Buch entstand aus einer Vorlesung, die er während Forschungsaufenthalten an der University of Sussex und an der Helsinki University of Sussex gehalten hat.

An Introduction To Differentiable Manifolds And Riemannian Geometry

Author : William Munger Boothby
ISBN : 0121160513
Genre : Mathematics
File Size : 68. 10 MB
Format : PDF
Download : 898
Read : 981

Get This Book


The second edition of this text has sold over 6,000 copies since publication in 1986 and this revision will make it even more useful. This is the only book available that is approachable by "beginners" in this subject. It has become an essential introduction to the subject for mathematics students, engineers, physicists, and economists who need to learn how to apply these vital methods. It is also the only book that thoroughly reviews certain areas of advanced calculus that are necessary to understand the subject. Line and surface integrals Divergence and curl of vector fields

Lectures On The Topology Of 3 Manifolds

Author : Nikolai Saveliev
ISBN : 9783110250367
Genre : Mathematics
File Size : 67. 59 MB
Format : PDF, Mobi
Download : 406
Read : 1137

Get This Book


This textbook – now in its second revised and extended edition – introduces the topology of 3- and 4-dimensional manifolds. It also considers new developments especially related to the Heegaard Floer and contact homology. The book is accessible to graduate students in mathematics and theoretical physics familiar with some elementary algebraic topology, including the fundamental group, basic homology theory, and Poincaré duality on manifolds.

A Geometric Approach To Differential Forms

Author : David Bachman
ISBN : 9780817683047
Genre : Mathematics
File Size : 47. 82 MB
Format : PDF, Docs
Download : 245
Read : 990

Get This Book


This text presents differential forms from a geometric perspective accessible at the undergraduate level. It begins with basic concepts such as partial differentiation and multiple integration and gently develops the entire machinery of differential forms. The subject is approached with the idea that complex concepts can be built up by analogy from simpler cases, which, being inherently geometric, often can be best understood visually. Each new concept is presented with a natural picture that students can easily grasp. Algebraic properties then follow. The book contains excellent motivation, numerous illustrations and solutions to selected problems.

Modern Geometric Structures And Fields

Author : Сергей Петрович Новиков
ISBN : 9780821839294
Genre : Mathematics
File Size : 50. 67 MB
Format : PDF, ePub, Mobi
Download : 307
Read : 164

Get This Book


The book presents the basics of Riemannian geometry in its modern form as geometry of differentiable manifolds and the most important structures on them. The authors' approach is that the source of all constructions in Riemannian geometry is a manifold that allows one to compute scalar products of tangent vectors. With this approach, the authors show that Riemannian geometry has a great influence to several fundamental areas of modern mathematics and its applications. In particular, Geometry is a bridge between pure mathematics and natural sciences, first of all physics. Fundamental laws of nature are formulated as relations between geometric fields describing various physical quantities. The study of global properties of geometric objects leads to the far-reaching development of topology, including topology and geometry of fiber bundles. Geometric theory of Hamiltonian systems, which describe many physical phenomena, led to the development of symplectic and Poisson geometry. Field theory and the multidimensional calculus of variations, presented in the book, unify mathematics with theoretical physics. Geometry of complex and algebraic manifolds unifies Riemannian geometry with modern complex analysis, as well as with algebra and number theory. Prerequisites for using the book include several basic undergraduate courses, such as advanced calculus, linear algebra, ordinary differential equations, and elements of topology.

Topology

Author : Solomon Lefschetz
ISBN : 0828401160
Genre : Mathematics
File Size : 83. 33 MB
Format : PDF, ePub, Docs
Download : 830
Read : 765

Get This Book



Grundlagen Der Analysis

Author : Edmund Landau
ISBN : 0828401411
Genre : Mathematics
File Size : 23. 51 MB
Format : PDF
Download : 420
Read : 703

Get This Book


Landau's classic book on the foundations of analysis is presented in its original German, with a German-English dictionary as an appendix. One intent of this edition is to provide the English-speaking mathematician with an opportunity to learn some mathematical German. Of course, a pleasant by-product is having Landau's exposition on the construction of the real numbers from the natural numbers using Dedekind cuts. The book is written in an extremely telegraphic style, with few words outside the 'Theorem-Proof' motif, making the German notably simpler than in more advanced texts. Thus, the student who begins this book with little or no knowledge of German will gain the experience of successfully reading an entire book in mathematics and with it a feeling for the language and a well-ingrained mathematical vocabulary. The English edition of the book is available as Foundations of Analysis.

Lectures On Differential Geometry

Author : Shlomo Sternberg
ISBN : 9780821813850
Genre : Mathematics
File Size : 40. 39 MB
Format : PDF, Kindle
Download : 317
Read : 1178

Get This Book


This book is based on lectures given at Harvard University during the academic year 1960-1961. The presentation assumes knowledge of the elements of modern algebra (groups, vector spaces, etc.) and point-set topology and some elementary analysis. Rather than giving all the basic information or touching upon every topic in the field, this work treats various selected topics in differential geometry. The author concisely addresses standard material and spreads exercises throughout the text. His reprint has two additions to the original volume: a paper written jointly with V. Guillemin at the beginning of a period of intense interest in the equivalence problem and a short description from the author on results in the field that occurred between the first and the second printings.

Sturm Liouville Operators And Applications

Author : V.A. Marchenko
ISBN : 9783034854856
Genre : Juvenile Nonfiction
File Size : 77. 26 MB
Format : PDF, ePub
Download : 569
Read : 1259

Get This Book



Top Download:

Best Books