Topology and Geometry for Physicists (Dover Books on Mathematics)

I must say that this wonderful little book must be (and I recommend it as such) the first step for a physicist into the world of higher geometry (manifolds, differential forms, stokes theorem, curvature, etc), differential and algebraic topology where topics like Homotopy, Homology, Cohomology theories, the theory of Fiber bundles, characteristic classes and Morse theory appear. The authors are brilliant expositors and know their subject well, they oftenly give handiful insights into the subjects being treated and write so beautiful it makes think you are reading a Tolkien's story!. I believe this book should be a classic, for example I found it cited on another good book about group theory for particle physics (Costa and Fogli, Symmetries and Group Theory in Particle Physics), it is also cited in Nakahara. The book ends with some more physics like Yang-Mills theories from a geometric perspective where concepts like instatons and monopoles are treated. After this title you will be in a better position to address more terse books like Nakahara which at times requires a bit more of mathematical maturity. If I have to resume I would say it has been beautifully and clearly written, all in all, simply brilliant!!

Stephen Hawking's "A brief history of time" talked conceptually about quantum mechanics and its relation to the universe. Mathematics is the link to comprehending the origin of the conclusions that have been reached. While I lack the expertise to work out rigorous mathematical proof, the mathematical ideas are made tangible and applicable in this text. In a search for meaning in the world of physics one necessarily needs a compass for direction and it rests with having the necessary mathematical tools to do so.

Good book.

The book presents several very interesting (and advanced) issues from topology and differential geometry with applications to (particle) physics. The book has been written for theoritical physicists which makes the book accessible to a large scientific public and not only for mathematician. The book is excellent. Many thanks.

Good introduction, but with several typos and unclear sections.

The very modest description of this used book's condition had me expecting less. It turned out to be in much better shape. The person, who sold the book, was definitely not trying to oversell it. I would buy another book from him any day.

I haven't actually read this book, but from just skimming it, I see that it contains no exercises at all. Without any exercises, it would be really hard to use this book for self study, and hope to retain the material. Based on the reviews, it looks like the better books available on the topic are "Geometry, Topology and Physics" by Nakahara, and "The Geometry of Physics: An Introduction" by Frankel.

It remains true that this text is absent exercises for students wishing to hone their problem solving skills. Still, the book remains an invaluable stepping stone to more advanced treatments. I first encountered this text (in the 1980's) after reading an article in Scientific American: Fiber Bundles and Quantum Theory (July 1981, Bernstein and Phillips). My interest in fiber bundles was cemented. Then, I searched for more information. The physics reports article "Gravitation, Gauge Theories and Differential Geometry" (Vol. 66, No.6,1980, Guchi, Gilkey, Hanson) was too advanced and detailed. Too brief was Yang's article: Geometry and Physics (Gauge Theories, Einstein Symposium,1981, pages 3-11). Imagine my happiness in finding the text of Nash and Sen. Falling (as it does) between two extremes--not too elementary, not too advanced-- not too brief and not too long. Here find 100 pages (chapter seven) devoted to the topic. In fact, I find the entire book refreshing. If one needs Exercises, Nakahara's 1999 textbook fits the bill. I offer an overview of my impressions:(1) Chapter One, Basic Notions of Topology, is just that--basic notions. Any 'notion' in this chapter can fill a book (for instance: First Concepts of Topology by Chin and Steenrod or Fixed Points, by Shashkin).(2) Chapter two: differential geometry, manifolds and differential forms. Now, those concepts consume entire books, so Nash and Sen will not replace more detailed textbooks (say, Spivak or Flanders).This is merely a beginning.(3) Fundamental Group, Homology, Cohomology (Chapters three to six), ninety pages of basic material. Glance at the proof of Poincare's lemma: one page in Nakahara (see page 196). More leisurely is Nash and Sen (see pages 125-127). Compare and contrast. Nash and Sen, as such, adds much clarity to Nakahara's exposition in other respects too. Nakahara "patterns" discussion of homology and homotopy upon Nash & Sen (see Nakahara, pages 61 and 89).(4) My favorite chapter (seven) is Fiber Bundles. Compare one instance: of Electromagnetism. Nakahara's (page 354) to Nash & Sen's (page 196).(5) Morse Theory, chapter eight. Again, introductory in character. A topic absent in both Nakahara and Eguchi, et.al. The book concludes with Yang-Mills theories and an interesting discussion of quaternions, instantons and twistors. That material is not duplicated (in this manner) in any of the other references for which I have offered direct comparison.(6) In retrospect, I have created an increasing tower of technicality in which to progress: read Bernstein's Scientific American article, then proceed to Yang's article (both are qualitative and beautiful). Study Nash and Sen concurrent with Nakahara (They complement each other wonderfully). Finally, study the Physics Reports article by Eguchi, Gilkey and Hanson (the pinnacle--at least, for me). But, no single resource will satisfy every need. However, Nash and Sen fills a much needed niche.