Differential Topology

by Morris W. Hirsch, Victor Guillemin, Alan Pollack
Differential Topology cover
Good Books rating 3.98
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  • ID: 7427
  • Added: 2025-12-14
  • Updated: 2025-12-14
  • ISBN: 9780821851937
  • Publisher: American Mathematical Soc.
  • Published: 2010-01-01
  • Reviews: 4

Differential Topology by Guillemin and Pollack offers an elementary and intuitive approach to the study of smooth manifolds. The book is renowned for its clear and accessible exposition, making complex concepts approachable with a balance of detail and generality. It is designed to be mostly self-contained, requiring only undergraduate-level analysis and linear algebra as prerequisites. The authors employ the unifying idea of transversality to avoid heavy machinery, making the main results more digestible. This approach allows for intelligent treatments of important theorems such as the Lefschetz fixed-point theorem, the Poincaré-Hopf index theorem, and Stokes theorem. /n/n The text is enriched with a variety of exercises that range from routine explorations to guided proofs of fundamental results. For instance, an exercise section in Chapter 4 leads students through the construction of de Rham cohomology and a proof of its homotopy invariance. The book is suitable for both introductory graduate courses and advanced undergraduate courses, making it a versatile resource for students and educators alike.

Reviews
abebooks.com · 2025-12-14
great 4.00

This book is celebrated for its excellent mathematical exposition and the right balance of detail and generality. It is considered a valuable resource for both beginners and advanced students.

The reviewer on abebooks.com highly recommends this book for its excellent mathematical exposition. They appreciate how the book strikes a perfect balance between detail and generality, making it accessible to a wide range of readers. Whether you are a beginner or an advanced student, this book is seen as a valuable resource that can enhance your understanding of differential topology. The reviewer's praise for the book's clarity and depth underscores its importance in the field.

Quick quotes

    A jewel of mathematical exposition.

    Judiciously picks the right mixture of detail and generality.

    Display the richness within the subject.

Goodreads · 2025-12-14
good 3.50

This book is praised for its accessible introduction to differential topology, making complex concepts understandable. It is recommended for those new to the subject but may lack depth for advanced readers.

The reviewers on Goodreads highlight that this book is an excellent starting point for anyone looking to dive into differential topology. It breaks down complex ideas into manageable parts, making it a great resource for beginners. However, they also note that while it's a solid introduction, it might not satisfy those seeking a more in-depth exploration of the subject. The book's strength lies in its clarity and approachability, which makes it a valuable addition to any mathematics library.

Quick quotes

    A great introduction to differential topology.

    Makes complex concepts understandable.

    Perfect for beginners but lacks depth for advanced readers.

Amazon · 2025-12-14
fine 4.40

This text is suitable for a second-year graduate mathematics course and is praised for its development of differentiable manifolds. It is described as a fine assembly of essential material.

The reviewer on Amazon commends this book for its suitability as a textbook for advanced graduate students. It is particularly noted for its clear and methodical development of the subject matter, making it an excellent resource for those studying differentiable manifolds. The book is praised for its comprehensive coverage and the way it presents complex topics in a structured and accessible manner. It is seen as a valuable tool for both students and educators in the field of mathematics.

Quick quotes

    Hirsch has assembled a very fine text which is suitable for a second year graduate mathematics course in differentiable manifolds.

    The development and presentation of the material is clear and structured.

    It is seen as a valuable tool for both students and educators in the field of mathematics.

Goodreads · 2025-12-14
valuable 4.00

This book is highly praised for its comprehensive and well-organized treatment of basic differential topology material. It is considered valuable for its concise yet thorough coverage.

The reviewer on Goodreads highlights that this book is a gem in the field of differential topology. Despite its relatively small size, it manages to cover a wide range of fundamental topics in a clear and organized manner. The book is particularly noted for its accessibility and the way it presents complex ideas in an understandable format. It is seen as an essential resource for anyone looking to grasp the basics of differential topology, making it a valuable addition to any mathematics library.

Quick quotes

    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.

    It is considered valuable for its concise yet thorough coverage.

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