Introduction to Differentiable Manifolds

Title: Introduction to Differentiable Manifolds
Author: Louis Auslander
ISBN: 9780486471723
Publisher: Dover Publications
Published: 2009
Binding: Paperback
Language: English
Edition: 2009
Number of Pages: 224
Condition Note: Clean, unmarked copy with some edge wear. Good binding. Dust jacket included if issued with one. We ship in recyclable American-made mailers. 100% money-back guarantee on all orders.
R: 1697247
Section: Mathematics | Geometry | Differential
Publisher Description: 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."