Differential Topology: First Steps (Dover Books on Mathematics) - Softcover

Andrew H. Wallace

Softcover

ISBN 10: 0486453170 ISBN 13: 9780486453170

Publisher: Dover Publications, 2006

Synopsis

Keeping mathematical prerequisites to a minimum, this undergraduate-level text stimulates students' intuitive understanding of topology while avoiding the more difficult subtleties and technicalities. Its focus is the method of spherical modifications and the study of critical points of functions on manifolds.
No previous knowledge of topology is necessary for this text, which offers introductory material regarding open and closed sets and continuous maps in the first chapter. Succeeding chapters discuss the notions of differentiable manifolds and maps and explore one of the central topics of differential topology, the theory of critical points of functions on a differentiable manifold. Additional topics include an investigation of level manifolds corresponding to a given function and the concept of spherical modifications. The text concludes with applications of previously discussed material to the classification problem of surfaces and guidance, along with suggestions for further reading and study.

About this title

About the Author

Andrew Wallace is Professor Emeritus in the Department of Mathematics at the University of Pennsylvania.

Edition details

• Publisher: Dover Publications
• Publication date: 2006
• Language: English
• ISBN 10: 0486453170
• ISBN 13: 9780486453170
• Binding: Paperback
• Number of pages: 158