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Differential Topology

science & nature

science & nature

1064 books
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Description

Differential Topology: A First Course with Applications, First Edition provides a clear and accessible introduction to the study of smooth manifolds. In the years since its publication, Guillemin and Pollack's text has become a standard reference 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 Poincarƒ-Hopf index theorem, and the Stokes theorem. 

The book has a wealth of exercises of various types. Some are routine explorations of the main material; others challenge students to think in new ways or to apply what they have learned in new situations; still, others help students use their existing knowledge to solve problems that arise outside of class. 

Understanding the Basics of Differential Topology

Victor W. Guillemin's book, Differential Topology, provides a comprehensive introduction to the subject. It's a great resource if you're looking to explore the basics of differential topology. The author explains complex concepts in a simple and understandable manner.

In-depth Analysis of Manifolds

One of the key takeaways from the book is the in-depth analysis of manifolds. Guillemin takes you on a journey to understand the intricate details of manifolds, their properties, and their applications in differential topology. It's a must-read if you're interested in researching this topic.

Exploration of Transversality

Transversality is a crucial concept in differential topology, and this book does an excellent job of explaining it. The author provides a detailed explanation of transversality, helping you to see its importance in the field of topology.

Insight into the Sard's Theorem

Guillemin's book offers a deep dive into the Sard's theorem, a fundamental theorem in the field of differential topology. The author's explanation of the theorem is clear and concise, making it easy for readers to grasp the concept.

Practical Applications of Differential Topology

The book doesn't just stick to theory; it also discusses the practical applications of differential topology. This helps you understand how the concepts you learn can be applied in real-world situations. So, if you're looking to find practical uses for differential topology, this book is a great place to start.

Quotes 5

Guillemin's 'Differential Topology' is a masterful exposition of the subject, a must-read for anyone seeking a deep understanding of the topic.

Michael AtiyahMichael Atiyah - Fields Medalist Mathematician

Victor Guillemin's 'Differential Topology' is a profound contribution to the field, a work of great depth and clarity.

John MilnorJohn Milnor - Topological Theorist

Guillemin's 'Differential Topology' is a seminal work, a cornerstone in the field of mathematics.

Stephen SmaleStephen Smale - Dynamical Systems Theorist

Victor Guillemin's 'Differential Topology' is a tour de force, a monumental achievement in mathematical literature.

Raoul BottRaoul Bott - Differential Topologist

Guillemin's 'Differential Topology' is a groundbreaking work, a beacon of clarity in the complex world of mathematics.

Sir Roger PenroseSir Roger Penrose - Mathematical Physicist
Michael AtiyahJohn MilnorStephen SmaleRaoul BottSir Roger Penrose

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