Algebraic Topology

Algebraic Topology cover
Good Books rating 3.12
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Technical
  • ID: 7384
  • Added: 2025-12-14
  • Updated: 2025-12-30
  • ISBN: 9780521795401
  • Publisher: Cambridge University Press
  • Published: 2002-01-01
  • Formats: 1
  • Reviews: 4

Algebraic Topology is a foundational textbook designed for graduate-level students and self-study, offering a broad and readable introduction to the subject. It covers essential topics such as the fundamental group, covering spaces, homology, cohomology, higher homotopy groups, and general homotopy theory, with a strong emphasis on geometric aspects to build intuition. The book is unique in its inclusion of many optional topics not typically covered in introductory courses, such as Bockstein and transfer homomorphisms, direct and inverse limits, H-spaces, Hopf algebras, the Brown representability theorem, and a full exposition of Steenrod squares and powers. These additional topics make the book valuable not only for students but also for researchers seeking detailed expositions of advanced subjects. The textbook is structured to facilitate both classroom use and independent study, with numerous examples and exercises to reinforce understanding. The author's clear and engaging writing style makes complex concepts more accessible, while the optional topics provide a deeper exploration for those interested in advancing their knowledge. Whether used in a course or for personal study, Algebraic Topology serves as an indispensable resource for anyone delving into this fascinating field of mathematics.

Reviews
Amazon · 2025-12-14
interesting 4.00

The book is enjoyed for its interesting content and useful crash reviews in algebra and analysis. It serves as a helpful reference for those studying the subject.

The reviewer found this book very interesting and enjoyable to read. They particularly appreciated the crash reviews in algebra and analysis, which they found to be very useful. These sections served as a helpful reference, making the book a valuable resource for those studying algebraic topology. The reviewer's positive experience suggests that the book is well-suited for those looking to deepen their understanding of the subject.


Quick quotes

    A very interesting book which I enjoyed.

    I particularly found useful the 'crash review' in algebra and analysis.

    This book functions as a useful reference for those studying algebraic topology.

Reddit - r/math · 2025-12-14
challenging 2.00

The book is found to be unreadable due to its rigorous style, making it difficult to follow the proofs. The reviewer suggests it may not be suitable for those seeking an accessible introduction to algebraic topology.

The reviewer, who appreciates the rigor of analysis, found this book extremely unreadable. They mentioned that reading proofs in this book feels like a daunting task, which might not be ideal for someone looking for an easy-to-follow introduction. The book's style is described as overly complex, which could be a barrier for many readers. However, it might be suitable for those who are already well-versed in the subject and are looking for a more challenging text.


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    As someone who likes the rigor of analysis, I find this book extremely unreadable.

    Reading proofs in this book for me feels like reading...

    This book may not be suitable for those seeking an accessible introduction to algebraic topology.

Math StackExchange · 2018-05-23
engaging 3.50

The book is engaging and draws interest in the subject despite some lack of rigor. It provides a good introduction to algebraic topology.

This review highlights that the book is not overly rigorous but still manages to capture the reader's interest in algebraic topology. It serves as a good starting point for those new to the subject, offering a panoramic view of the basic theories. The reviewer appreciates the book's ability to spark curiosity and provide a solid foundation in the field. However, they note that some parts can be unclear, which might require additional resources to fully grasp the concepts.


Quick quotes

    I really liked the book: it was not rigorous (somewhat unclear at some places) but enough to draw my interest in the subject.

    A cursory glance through the book suggests it is has a strong differential flavour.

    This book is a delight introduction to algebraic topology.

Reddit · 2013-07-08
enjoyable 3.00

While not a fun read cover to cover, individual chapters are enjoyable and make for leisurely reading.

This book might not be the most engaging read from cover to cover, but it shines when read chapter by chapter. Each chapter offers enjoyable and leisurely reading, making it a valuable resource for those willing to take their time. The book's structure allows for a more relaxed approach, which can be beneficial for understanding complex topics. Overall, it's a worthwhile resource for those interested in algebraic topology.


Quick quotes

    I don't think it's a very fun book to read beginning to end, but individual chapters make for very leisurely reading.

    May is good but I think a ...

    I've heard great things about this book - how it's by far the most readable book in introductory algebraic topology, beautiful typesetting, builds up from ...