Topology of Surfaces, Knots, and Manifolds
January 2001, ©2001
Topology of Surfaces, Knots, and Manifolds offers an intuition-based and example-driven approach to the basic ideas and problems involving manifolds, particularly one- and two-dimensional manifolds. A blend of examples and exercises leads the reader to anticipate general definitions and theorems concerning curves, surfaces, knots, and links-the objects of interest in the appealing set of mathematical ideas known as "rubber sheet geometry." The result is a text that is accessible to a broad range of undergraduate students, yet still provides solid coverage of the mathematics underlying these topics.
* Classification of Compact Surfaces
* Putting More Structure on Surfaces
* Graphs and Topology
* Knot Theory
- A student-friendly writing style provides a clear exposition of concepts.
- Mathematical results are presented accurately and main definitions, theorems, and remarks are clearly highlighted for easy reference.
- Carefully selected exercises, some of which require hands-on work or computer-aided visualization, reinforce the understanding of concepts or further develop ideas.
- Extensive use of illustrations helps the students develop an intuitive understanding of the material.
- Frequent historical references chronicle the development of the subject and highlight connections between topology and other areas of mathematics.
- Chapter summary sections offer a review of each chapter's topics and a transitional look forward to the next chapter.