Manifolds, Groups, Bundles, and Spacetime

Front Cover
Lulu.com, Jul 23, 2015 - Science - 418 pages
Manifolds, Groups, Bundles, and Spacetime was written for those who are interested in modern differential geometry and its applications in physics. The primary material is suitable for a graduate level course in the theory of differentiable manifolds, Lie groups, and fiber bundles. The first two chapters are an introduction to concepts from linear algebra and tensors and can be read to establish familiarity with the notation and conventions of the text by those who are already familiar with these topics. The third and fourth chapters are a review of topics from advanced calculus and topology and are included primarily as a convenient reference.
 

Contents

TOPICS FROM LINEAR ALGEBRA
1
MULTILINEAR ALGEBRA
25
DIFFERENTIAL CALCULUS ON VECTOR SPACES
57
DIFFERENTIABLE MANIFOLDS
127
TOPOLOGY
149
DIFFERENTIAL CAL CULUS ON MANIFOLDS
165
LIE GROUPS AND LIE ALGEBRAS
207
FIBER BUNDLES
235
THE DIFFERENTIAL GEOMETRY OF SPACETIME
291
INTEGRATION ON MANIFOLDS
317
INTRODUCTION TO GENERAL RELATIVITY
353
PICARDS THEOREM
379
References
399
Copyright

Common terms and phrases

Bibliographic information