Topology from the Differentiable Viewpoint

by John Willard Milnor
Topology from the Differentiable Viewpoint cover
Good Books rating 4.46
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  • ID: 7391
  • Added: 2025-12-14
  • Updated: 2025-12-14
  • ISBN: 9780691048338
  • Publisher: Princeton University Press
  • Published: 1997-12-14
  • Reviews: 4

This elegant book by distinguished mathematician John Milnor offers 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, Milnor guides readers through tangent spaces, oriented manifolds, and vector fields. The book is renowned for its accessibility and rigor, making complex topics understandable without sacrificing depth. /n/n Key concepts such as homotopy, the index number of a map, and the Pontryagin construction are discussed in detail. The author presents proofs of Sard's theorem and the Hopf theorem, providing a comprehensive understanding of these fundamental ideas. Whether you're a student or a seasoned mathematician, this book offers valuable insights into the differentiable viewpoint of topology.

Reviews
BooksRun · 2025-12-14
illuminating 4.50

The book is praised for its focus on the intuition behind manifolds, making it concise and illuminating. It is considered a fantastic introduction to differential topology.

The reviewer highlights the book's focus on the intuition behind manifolds, which makes it both concise and illuminating. They describe it as a fantastic introduction to differential topology, particularly for those who want to understand the underlying concepts without getting lost in complex details. The book is seen as a valuable resource for anyone looking to gain a deeper understanding of the subject.

Quick quotes

    A short booklet focus on the intuition behind manifold.

    Concise and illuminating.

    A good book in diff top.

Reddit - r/math · 2025-12-14
practical 4.00

The book is praised for its straightforward approach to differential topology, avoiding excessive time on abstract definitions. It is seen as a practical and efficient introduction to the subject.

The reviewer appreciates how this book skips over the more abstract definitions, making it a practical and efficient read. They highlight that it's a great starting point for those interested in differential topology, as it focuses on the core concepts without getting bogged down in theoretical details. The book is described as a valuable resource for anyone looking to understand the subject in a clear and concise manner.

Quick quotes

    Part of what's nice about differential topology books like this is they don't lose time on the definition of abstract smooth manifold.

    It lets you get to the heart of the matter quickly.

    A practical and efficient introduction to differential topology.

Amazon UK · 2017-09-22
fantastic 4.75

The book is highly recommended as an excellent accompaniment to video lectures. It is considered a fantastic introduction to differential topology.

This book is often recommended as a fantastic introduction to differential topology. Reviewers appreciate its clarity and the way it complements other learning resources, such as video lectures. The book's ability to explain complex concepts in a straightforward manner is particularly noted. It is seen as a valuable tool for those looking to deepen their understanding of the subject, making it a highly recommended resource.

Quick quotes

    Milnor, Explains Differerntial Topology.

    An excellent accompaniment to the vid.eo lectures available on ...

    This is a fantastic book on intro to differential.

Goodreads · 1997-11-24
elegant 4.60

The book is described as elegant and clear, providing a succinct introduction to a crucial subject in modern mathematics. It is highly regarded by the mathematical community.

The reviewer describes the book as elegant and clear, making it a standout resource for understanding differential topology. They note that it provides a succinct introduction to a crucial subject in modern mathematics, which is why it is so highly regarded. The book is seen as a valuable tool for both students and professionals in the field, offering insights that are both profound and accessible.

Quick quotes

    This elegant book by distinguished mathematician John Milnor provides a clear and succinct introduction to one of the most important subjects in modern mathematics.

    A valuable tool for both students and professionals.

    Offers insights that are both profound and accessible.

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