Differential geometry and topology have become essential tools for many theoretical physicists. In particular, they are indispensable in theoretical studies of condensed matter physics, gravity, and particle physics. Geometry, Topology and Physics, Second Edition introduces the ideas and techniques of differential geometry and topology at a level suitable for postgraduate students and researchers in these fields.
The second edition of this popular and established text incorporates a number of changes designed to meet the needs of the reader and reflect the development of the subject. The book features a considerably expanded first chapter, reviewing aspects of path integral quantization and gauge theories. Chapter 2 introduces the mathematical concepts of maps, vector spaces, and topology. The following chapters focus on more elaborate concepts in geometry and topology and discuss the application of these concepts to liquid crystals, superfluid helium, general relativity, and bosonic string theory. Later chapters unify geometry and topology, exploring fiber bundles, characteristic classes, and index theorems. New to this second edition is the proof of the index theorem in terms of supersymmetric quantum mechanics. The final two chapters are devoted to the most fascinating applications of geometry and topology in contemporary physics, namely the study of anomalies in gauge field theories and the analysis of Polakov’s bosonic string theory from the geometrical point of view.
Reviews (5)
5 reviews for Geometry, Topology and Physics
AStudent
Rated 5 out of 5
November 20, 2022
My entire Differential Geometry course was based upon this book so I relented and splashed out a bit to get myself my own copy that I can annotate fre...More
My entire Differential Geometry course was based upon this book so I relented and splashed out a bit to get myself my own copy that I can annotate freely. I bought a second hand copy for ~£52 and it came in perfect condition. My seller was kind enough to wrap it tightly in plastic to prevent any damage during transport and the pages were not marked or damaged at all.
I personally really enjoy the way this text has been written there's enough detail in the theory to the point were it satisfies me as reader but not so much repetition that it becomes drab. Concise, detailed and thorough in the theorems and proofs presented. Enough exercises to satisfy the passing reader but I guess you can always wish for more :D Hopefully those will get supplemented by your professor. But as always with most graduate student books they are there as a detailed 'dictionary' if you will - not so much as an exercise book.
If you want something that covers all bases in your beginners quest of Differential Geometry this is the book for you!
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ASanders
Rated 5 out of 5
March 10, 2021
If you, as a pathetic physics student that stopped taking maths classes after undergrad topology, have ever wanted a mathematical physicist to beat yo...More
If you, as a pathetic physics student that stopped taking maths classes after undergrad topology, have ever wanted a mathematical physicist to beat you about the head with a blunt instrument until you understood how to express physics ideas in the language of Riemannian geometry then this is the book for you. 10/10 would get flexed on by Nakahara again
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NAgwu
Rated 5 out of 5
September 24, 2019
The book is easy to read; provides a lot of examples.
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potatocake
Rated 5 out of 5
January 22, 2019
Nakahara is quite a clear book. The logic is very tight and organized and the exercises are nice - they are short and easy, just to check your underst...More
Nakahara is quite a clear book. The logic is very tight and organized and the exercises are nice - they are short and easy, just to check your understanding. It is a good idea to do all of the exercises because there are not many of them. It is one of the more rigorous "math for physicists" books I have read.
There are indeed some mistakes, but you should be able to find them. One good thing is that Nakahara points out the physical interpretation of things, like homotopy, so you can get a intuitive feel. A great book!
The only complaint I have is that the references are pretty bad. Nakahara likes to cite Japanese books which I do not have access to and, anyway, are in Japanese. I wish he would cite classic books that everyone uses.
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Debmalya
Rated 5 out of 5
May 18, 2018
Yes I got it with a excellent quality.
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I personally really enjoy the way this text has been written there's enough detail in the theory to the point were it satisfies me as reader but not so much repetition that it becomes drab. Concise, detailed and thorough in the theorems and proofs presented. Enough exercises to satisfy the passing reader but I guess you can always wish for more :D Hopefully those will get supplemented by your professor. But as always with most graduate student books they are there as a detailed 'dictionary' if you will - not so much as an exercise book.
If you want something that covers all bases in your beginners quest of Differential Geometry this is the book for you!
There are indeed some mistakes, but you should be able to find them. One good thing is that Nakahara points out the physical interpretation of things, like homotopy, so you can get a intuitive feel. A great book!
The only complaint I have is that the references are pretty bad. Nakahara likes to cite Japanese books which I do not have access to and, anyway, are in Japanese. I wish he would cite classic books that everyone uses.