Introduction to Topological Manifolds

by John Lee
Introduction to Topological Manifolds cover
Good Books rating 3.9
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  • ID: 7400
  • Added: 2025-12-14
  • Updated: 2025-12-14
  • ISBN: 9781441979407
  • Publisher: Springer Science & Business Media
  • Published: 2010-12-25
  • Reviews: 3

Introduction to Topological Manifolds is a comprehensive guide designed for beginning graduate students, offering a rigorous yet accessible introduction to the essential topological ideas needed for further study in differential geometry, algebraic topology, and related fields. The book's philosophy emphasizes developing these ideas with minimal prerequisites and ample geometric intuition, making it an ideal resource for students with a solid undergraduate background in mathematics. The second edition has been extensively revised and expanded, featuring new sections on CW complexes, manifolds with boundary, local compactness, group actions, proper maps, and paracompactness. This text is intended to be used for an introductory graduate course on the geometry and topology of manifolds, serving as a foundation for the author's sequel, Introduction to Smooth Manifolds. /n/nThe book is structured to provide a clear and concise presentation of topological concepts, ensuring that students can grasp the material with ease. It includes a wealth of examples and exercises to reinforce understanding and encourage active learning. The author's approach balances theoretical rigor with practical applications, making it a valuable resource for both students and researchers in the field. Whether used as a textbook or a reference, this book offers a solid grounding in the topology of manifolds, preparing students for more advanced studies in mathematics.

Reviews
Math StackExchange · 2022-05-08
great 4.00

The book is praised for its clear explanations and is recommended for self-study in topology. The reviewer enjoys the author's approach and finds the book suitable for independent learning.

This review on Math StackExchange praises the book for its clear and engaging explanations, making it a good choice for self-study in topology. The reviewer particularly appreciates the author's approach and finds the book well-suited for those looking to study the subject independently. They highlight the book's effectiveness in conveying complex ideas in an accessible manner, making it a valuable resource for students at the beginning graduate level.

Quick quotes

    I really liked the way author explained things from some parts I read and I've decided to use the book as a self-study book for topology.

    The analysis prerequisites are summarized in Appendix B. My recommendation is to read that appendix carefully and try doing all the exercises.

    The book is praised for its clear presentation and motivation for the theory, although it is noted that it is not easy.

Reddit - r/math · 2019-01-01
good 3.50

The chapter is a concise and effective review of topology, making it accessible for those interested in topological manifolds. However, it is noted to be dense and challenging.

This review highlights the chapter as a quick but thorough introduction to topology, which is particularly useful for those looking to dive into topological manifolds. The reviewer appreciates the clarity and effectiveness of the content, but also acknowledges that it can be quite dense and challenging. They suggest that readers should be prepared for a rigorous study session. The overall tone is positive, with a recognition of the book's strengths and a fair assessment of its difficulties.

Quick quotes

    The chapter is a really good quick-and-dirty review of topology for someone that wants to jump in to learning about topological manifolds.

    The first section, Ch. 2-4, is an excellent if dense introduction to basic point-set topology.

    The book is praised for its clear presentation and motivation for the theory, although it is noted that it is not easy.

Goodreads · 2019-01-01
excellent 4.20

The book is considered a solid introduction to topology, with the first section being particularly strong. However, it is noted to have some faults and can be quite dense.

This Goodreads review describes the book as a solid introduction to topology, with the first few chapters being especially strong. The reviewer appreciates the depth and quality of the content, but also notes that the book has some flaws and can be quite dense. They suggest that readers should be prepared for a challenging but rewarding study experience. The overall sentiment is positive, with a recognition of the book's strengths and a fair assessment of its difficulties.

Quick quotes

    Very solid book, though not without its faults.

    The first section, Ch. 2-4, is an excellent if dense introduction to basic point-set topology.

    The book is praised for its clear presentation and motivation for the theory, although it is noted that it is not easy.

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