# [Reading] ➼ Geometry, Topology and Physics, Second Edition (Graduate Student Series in Physics) ➲ Mikio Nakahara – Tactical-player.co.uk

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 FieldsThe 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 Introduces The Mathematical Concepts Of Maps, Vector Spaces, And Topology The Following Chapters Focus On 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 ViewGeometry, Topology And Physics, Second Edition Is An Ideal Introduction To Differential Geometry And Topology For Postgraduate Students And Researchers In Theoretical And Mathematical Physics

I must say that this edition contains some severe errors In several places the mathematics has been wrongly transferred over from the old edition in key definitions such as those of the wedge product those should be tensor products on the RHS and topological spaces that s a J in ii , not a T and elsewhere in the book I m not sure how many there are in total so I write this as a caution t

I think this is a nice book for people who start work in the area of mathematical physics The content of the first chapter gives a broad introduction to quantum mechanics paying special attention to path integral quantization The rest of the book deals mainly with topology homology groups, homotopy classes, topological invariants like Chern numbers, etc and its application in quantum fiel

To complete this book, there should be a section on general curvilinear coordinate transformations, the ultimate foundation of tensor calculus.This is a defficiency this book shares with many differential geometry texts.But maybe this can be forgiven at graduate level, for which this book is a decent pedagogical text if a little terse at times.The book begins with a survey of those areas o

Nakahara s book is one of the best introductions to geometry and topology that I have read I constantly use the book as the starting place for just about any topic in geometry and topolgy.After reading the book you will not be able to jump straight into research work, but it does bridge the gap between advanced texts and papers.Everybody should have a copy.

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 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 Naka

This is the best book of its type, that is, a book that contains almost all if not all the advance mathematics a theoretical physicist should know I have studied chapters 2 9 and it has the perfect balance between rigorous presentation of topics and practical uses with examples The level is for advance graduate students The range of topics covered is wide including Topology topics like Homoto

The book is well explained Topics are introduced in a progressive way, allowing the reader to adjust to new concepts before applying them in elaborate scenarios The author often mention practical applications of mathematical concepts that otherwise look disconnected to physics or any other field There are few typos and, from my point of view, many figures need a better caption description.

The book is easy to read provides a lot of examples.

I am surprised that amidst all the glowing reviews, there is only one reviewer who points out the unacceptable number of errata in this book A couple of misprints here and there throughout the whole book or even per chapter would be acceptable, but I agree with the other reviewer that at times, the misprints are as much as one per page In addition to the error on page 56 equation 1.241d should h