Introduction to Topology and Geometry (Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts)

A sweeping yet uniquely accessible introduction to a variety of central geometrical topics Covering over two centuries of innovations in many of the central geometrical disciplines, Introduction to Topology and Geometry is the most comprehensive introductory-level presentation of modern geometry currently available. Unique in both style and scope, the book covers an unparalleled range of topics, yet strikes a welcome balance between academic rigor and accessibility. By including subject matter previously relegated to higher-level graduate courses in mathematics and making it both interesting and accessible, the author presents a complete and cohesive picture of the science for students just entering the field. Historical notes throughout provide readers with a feel for how mathematical disciplines and theorems come into being. Students and teachers will benefit from a uniquely unified treatment of such topics as: Homeomorphism Graph theory Surface topology Knot theory Differential geometry Riemannian geometry Hyperbolic geometry Algebraic topology General topology Using a variety of theorems to tie these seemingly disparate topics together, the author demonstrates the essential unity of mathematics. A logical yet flexible organization makes the text useful for courses in basic geometry as well as those with a more topological focus, while exercises ranging from the routine to the challenging make the material accessible at varying levels of study.