Manifold Theory: An Introduction for Mathematical Physicists

Front Cover
Horwood Publishing, Mar 15, 2002 - Mathematics - 423 pages
This account of basic manifold theory and global analysis, based on senior undergraduate and post-graduate courses at Glasgow University for students and researchers in theoretical physics, has been proven over many years. The treatment is rigorous yet less condensed than in books written primarily for pure mathematicians. Prerequisites include knowledge of basic linear algebra and topology. Topology is included in two appendices because many courses on mathematics for physics students do not include this subject.

  • Provides a comprehensive account of basic manifold theory for post-graduate students
  • Introduces the basic theory of differential geometry to students in theoretical physics and mathematics
  • Contains more than 130 exercises, with helpful hints and solutions
 

Contents

Tensor algebra
26
Exercises 2
58
Vector and tensor fields on a manifold
88
Exterior differential forms
114
Exercises 5
142
3
154
Exercises 6
177
Symplectic manifolds
239
Exercises 9
282
Exercises 10
301
Complex linear algebra Almost complex manifolds
349
Anayltic topology
375
Quaternions and Cayley numbers
396
Homotopy review
404
Some answers some hints and some fragmentary solutions to the exercises
412
Index
419

Lie groups
249

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About the author (2002)

Daniel Martin, Glasgow University, UK