Geometry, Topology and Physics

by Mikio Nakahara

This textbook provides an introduction to the ideas and techniques of differential geometry and topology. It starts with a brief survey of the physics needed to follow the arguments - including quantum field theory, gauge theory and general relativity - to make sure all readers set off from the same starting point. Basic theory of vector spaces and topology is also included to make the book self-contained. Working from the basics to the more elaborate concepts of topology and geometry, all is carefully explained and illustrated with applications. Explicit calculations and diagrams clarify the abstract ideas involved. Many illustrations, exercises and problems are included. This book will be invaluable to advanced undergraduates and researchers in many areas of physics.

Genres: Physics, Mathematics, Geometry

505 pages, Paperback

First published January 1, 1990

Reviews

[Bradley Gram-hansen · Rating 5 out of 5]

I now understand why so many recommend this text book. It is a fantastic book for getting to grips with differential geometry with lots of examples, pictures and exercises. It is written in a really nice format to. What also is nice and quite surprising about the book , is that despite the word "physics" being in the title, there is actually a lot of physics in it, which I wasn't expecting (but was a nice surprise) given the nature of the book! Within this book there is not only a whole course on DG, but a good guide to advanced quantum mechanics and introductory relativity. There is also a good guide to some introductory and advanced topics within quantum field theory. For the price of this book and its given clarity, it is a bargin!

[Brian Powell · Rating 5 out of 5]

This book is a gateway drug. If you see a loved one reading this text, and especially if they deny having thoughts about string theory, they have a problem. There is a very narrow window of time to steer them towards less damaging theories of quantum gravity; if you’re too late, they will fall relentlessly into the deep well of billions upon billions upon billions of background-dependent, perturbatively renormalizable theories. Like light from a black hole this theory can’t explain, they will be doomed for all eternity.

[Renbao Liu · Rating 4 out of 5]

In general it is good. It is too brief in the last 4 chapters on the advanced topics (characteristic classes, index theorem, anomaly, bosonic string), which, understandably though, read like a quick survey.

[Lulu]

Geometry and topology for physicists