Topology of Surfaces, Knots, and Manifolds [Hardcover]

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.

Introduction and Intuitive Ideas

Manifolds

Classification of Compact Surfaces

Putting More Structure on Surfaces

Graphs and Topology

Knot Theory

Stephan C. Carlson is the author of Topology of Surfaces, Knots, and Manifolds, published by Wiley.Master the basic ideas of the topology of manifolds

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 will provides solid coverage of the mathematics underlying these topics.

Here are some of the features that make Carlson's approach work:

• A student-friendly writing style provides a clear exposition of concepts.
• mathematical results are presented accurately and main definitions,l#%