Differential topology
Author(s)
Bibliographic Information
Differential topology
AMS Chelsea Publishing, 2010
Available at / 13 libraries
-
Etchujima library, Tokyo University of Marine Science and Technology工流通情報システム
415.7/G92201751129
-
No Libraries matched.
- Remove all filters.
Note
Includes bibliographical references (p. 212-215) and index
Originally published: Englewood Cliffs, N.J. : Printice-Hall, 1974
Description and Table of Contents
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 Poincare-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.
by "Nielsen BookData"