Includes bibliographical references (pages 391-395) and index
Topology of subsets of Euclidean space -- Topological surfaces -- Simplicial surfaces -- Curves in R³ -- Smooth surfaces -- Curvature of smooth surfaces -- Geodesics -- The Gauss-Bonnet theorem
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The uniqueness of this text in combining geometric topology and differential geometry lies in its unifying thread: the notion of a surface. With numerous illustrations, exercises and examples, the student comes to understand the relationship of the modern abstract approach to geometric intuition. The text is kept at a concrete level, avoiding unnecessary abstractions, yet never sacrificing mathematical rigor. The book includes topics not usually found in a single book at this level
First course in geometric topology and differential geometry.