Geometry, topology, and physics

Mikio Nakahara9780750306065, 0750306068

Assuming a familiarity with quantum field theory and relativity, Nakahara (physics, Kinki University) explains the basic concepts of algebraic topology and differential geometry, defines the various types of fiber bundles and connections on fiber bundles, and applies the methods to anomalies appearing in gauge theories. The second edition adds the proof of the index theorem in terms of supersymmetric quantum mechanics. Distributed in the U.S. by AIDC.

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Table of contents :
EEn……Page 1
Front Cover……Page 2
Back Cover……Page 3
Copyright Info……Page 7
Dedication……Page 8
TOC……Page 9
Preface to the First Edition……Page 19
Preface to the Second Edition……Page 21
How to Read this Book……Page 23
Notation and Conventions……Page 24
1 – Quantum Physics……Page 25
2 – Mathematical Preliminaries……Page 91
3 – Homology Groups……Page 117
4 – Homotopy Groups……Page 145
5 – Manifolds……Page 193
6 – De Rham Cohomology Groups……Page 250
7 – Riemannian Geometry……Page 268
8 – Complex Manifolds……Page 332
9 – Fibre Bundles……Page 372
10 – Connections on Fibre Bundles……Page 398
11 – Characteristic Classes……Page 443
12 – Index Theorems……Page 477
13 – Anomalies in Gauge Field Theories……Page 525
14 – Bosonic String Theory……Page 552
References……Page 584
Index……Page 589