nLab Geometry, Topology and Physics


This page collects material related to the textbook

  • Mikio Nakahara,

    Geometry, Topology and Physics,

    First Edition: Institute of Physics Publishing, 1990. ISBN 0-85274-094-8 (hardcover), 0-85274-095-6 (paperback)

    Second Edition: Institute of Physics Publishing, 2003. ISBN: 9780750306065 (paperback), 9781138413368 (hardcover)



on geometry and topology in mathematical physics, such as in fiber bundles in physics.


Quantum Physics

Mathematical Preliminaries

Homology Groups

Homotopy Groups

Abelian groups

Simplices and simplicial complexes

Homology groups of simplicial complexes

General properties of homology groups


de Rham Cohomology Groups

Riemannian Geometry

Complex Manifolds

Fibre Bundles

Connections on Fiber Bundles

Connections on principal bundles



The covariant derivative

Gauge theories

Berry’s phase

Characteristic Classes

Index Theorems

Anomalies in Gauge Field Theories

Bosonic String Theory

category: reference

Last revised on July 15, 2022 at 21:31:40. See the history of this page for a list of all contributions to it.