Topology from the Differentiable Viewpoint

Author: John Willard Milnor
Publisher: Princeton University Press
ISBN: 9780691048338
Category : Mathematics
Languages : en
Pages : 80

Book Description
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.

Differential Topology

Author: Morris W. Hirsch
Publisher: Springer Science & Business Media
ISBN: 146849449X
Category : Mathematics
Languages : en
Pages : 230

Book Description
"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

Geometry from a Differentiable Viewpoint

Author: John McCleary
Publisher: Cambridge University Press
ISBN: 0521116074
Category : Mathematics
Languages : en
Pages : 375

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

Differential Topology

Author: Victor Guillemin
Publisher: American Mathematical Soc.
ISBN: 0821851934
Category : Mathematics
Languages : en
Pages : 242

Book Description
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

Author: Theodor Bröcker
Publisher: Cambridge University Press
ISBN: 9780521284707
Category : Mathematics
Languages : en
Pages : 176

Book Description
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.

Calculus on Manifolds

Author: Michael Spivak
Publisher: Westview Press
ISBN: 9780805390216
Category : Science
Languages : en
Pages : 164

Book Description
This book uses elementary versions of modern methods found in sophisticated mathematics to discuss portions of "advanced calculus" in which the subtlety of the concepts and methods makes rigor difficult to attain at an elementary level.

Introduction to Smooth Manifolds

Author: John M. Lee
Publisher: Springer Science & Business Media
ISBN: 0387217525
Category : Mathematics
Languages : en
Pages : 646

Book Description
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

Introduction to Topological Manifolds

Author: John M. Lee
Publisher: Springer Science & Business Media
ISBN: 038722727X
Category : Mathematics
Languages : en
Pages : 395

Book Description
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.

An Introduction to Manifolds

Author: Loring W. Tu
Publisher: Springer Science & Business Media
ISBN: 1441974008
Category : Mathematics
Languages : en
Pages : 426

Book Description
Manifolds, the higher-dimensional analogs of smooth curves and surfaces, are fundamental objects in modern mathematics. Combining aspects of algebra, topology, and analysis, manifolds have also been applied to classical mechanics, general relativity, and quantum field theory. In this streamlined introduction to the subject, the theory of manifolds is presented with the aim of helping the reader achieve a rapid mastery of the essential topics. By the end of the book the reader should be able to compute, at least for simple spaces, one of the most basic topological invariants of a manifold, its de Rham cohomology. Along the way, the reader acquires the knowledge and skills necessary for further study of geometry and topology. The requisite point-set topology is included in an appendix of twenty pages; other appendices review facts from real analysis and linear algebra. Hints and solutions are provided to many of the exercises and problems. This work may be used as the text for a one-semester graduate or advanced undergraduate course, as well as by students engaged in self-study. Requiring only minimal undergraduate prerequisites, 'Introduction to Manifolds' is also an excellent foundation for Springer's GTM 82, 'Differential Forms in Algebraic Topology'.

Manifolds, Sheaves, and Cohomology

Author: Torsten Wedhorn
Publisher: Springer
ISBN: 3658106336
Category : Mathematics
Languages : en
Pages : 366

Book Description
This book explains techniques that are essential in almost all branches of modern geometry such as algebraic geometry, complex geometry, or non-archimedian geometry. It uses the most accessible case, real and complex manifolds, as a model. The author especially emphasizes the difference between local and global questions. Cohomology theory of sheaves is introduced and its usage is illustrated by many examples.