Introduction to Differentiable Manifolds (Dover Books on Mathematics) - Softcover

Louis Auslander; Robert E. MacKenzie

Softcover

ISBN 10: 0486471721 ISBN 13: 9780486471723

Publisher: Dover Publications, 2009

Synopsis

The first book to treat manifold theory at an introductory level, this text surveys basic concepts in the modern approach to differential geometry. The first six chapters define and illustrate differentiable manifolds, and the final four chapters investigate the roles of differential structures in a variety of situations.
Starting with an introduction to differentiable manifolds and their tangent spaces, the text examines Euclidean spaces, their submanifolds, and abstract manifolds. Succeeding chapters explore the tangent bundle and vector fields and discuss their association with ordinary differential equations. The authors offer a coherent treatment of the fundamental concepts of Lie group theory, and they present a proof of the basic theorem relating Lie subalgebras to Lie subgroups. Additional topics include fiber bundles and multilinear algebra. An excellent source of examples and exercises, this graduate-level text requires a solid understanding of the basic theory of finite-dimensional vector spaces and their linear transformations, point-set topology, and advanced calculus.  

About this edition

• Publisher: Dover Publications
• Publication date: 2009
• ISBN 10: 0486471721
• ISBN 13: 9780486471723
• Binding: Paperback
• Number of pages: 224