Differential Topology
Seiten
1974
American Mathematical Society (Verlag)
978-1-4704-8112-4 (ISBN)
American Mathematical Society (Verlag)
978-1-4704-8112-4 (ISBN)
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Exploring smooth manifolds with clarity, the text employs transversality to illuminate differential topology. Pivotal results such as the Lefschetz, Poincaré–Hopf, and Stokes theorems are presented alongside diverse exercises that guide readers through proofs, including a derivation of the Jordan–Brouwer separation theorem.
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.
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.
Victor Guillemin, Massachusetts Institute of Technology, Cambridge, MA and Alan Pollack
Chapters
Chapter 1. Manifolds and smooth maps
Chapter 2. Transversality and intersection
Chapter 3. Oriented intersection theory
Chapter 4. Integration on manifolds
Appendix 1. Measure zero and Sard's theorem
Appendix 2. Classification of compact one-manifolds
| Erscheinungsdatum | 14.10.2025 |
|---|---|
| Reihe/Serie | AMS Chelsea Publishing |
| Verlagsort | Providence |
| Sprache | englisch |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Geometrie / Topologie |
| ISBN-10 | 1-4704-8112-X / 147048112X |
| ISBN-13 | 978-1-4704-8112-4 / 9781470481124 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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