"This volume, written by someone who has made many significant contributions to mathematical physics, not least to the present dialogue between mathematicians and physicists, aims to present some of the basic material in algebraic topology at the level of a fairly sophisticated theoretical physics graduate student. The most important topics, covering spaces, homotopy and homology theory, degree theory fibrations and a little about Lie groups are treated at a brisk pace and informal level. Personally I found the style congenial.(...) extremely useful as background or supplementary material for a graduate course on geometry and physics and would also be useful to those contemplating giving such a course. (...)" Contemporary Physics, A. Schwarz GL 308
Author(s): Albert S. Schwarz (auth.)
Series: Grundlehren der mathematischen Wissenschaften 308
Edition: 1
Publisher: Springer-Verlag Berlin Heidelberg
Year: 1994
Language: English
Pages: 296
Tags: Manifolds and Cell Complexes (incl. Diff.Topology);Quantum Information Technology, Spintronics;Quantum Physics
Front Matter....Pages I-XI
Background....Pages 1-17
Fundamental Concepts....Pages 19-32
The Degree of a Map....Pages 33-43
The Fundamental Group and Covering Spaces....Pages 45-57
Manifolds....Pages 59-75
Differential Forms and Homology in Euclidean Space....Pages 77-100
Homology and Cohomology....Pages 101-157
Homotopy Classification of Maps of the Sphere....Pages 159-166
Homotopy Groups....Pages 167-172
Fibered Spaces....Pages 173-183
Fibrations and Homotopy Groups....Pages 185-189
Homotopy Theory of Fibrations....Pages 191-207
Lie Groups....Pages 209-216
Lie Algebras....Pages 217-231
Topology of Lie Groups and Homogeneous Manifolds....Pages 233-242
Geometry of Gauge Fields....Pages 243-285
Back Matter....Pages 287-299
