Describing a striking connection between topology and algebra, rather than only proving the theorem, this study demonstrates how the result fits into a more general pattern. Throughout the text emphasis is on the interplay between algebra and topology, with graphical interpretation of algebraic operations, and topological structures described algebraically in terms of generators and relations. Includes numerous exercises and examples.

Describing a striking connection between topology and algebra, rather than only proving the theorem, this study demonstrates how the result fits into a more general pattern. Throughout the text emphasis is on the interplay between algebra and topology, with graphical interpretation of algebraic operations, and topological structures described algebraically in terms of generators and relations. Includes numerous exercises and examples.

This book is an elementary introduction to some ideas and techniques that have revolutionized enumerative geometry: stable maps and quantum cohomology. A striking demonstration of the potential of these techniques is provided by Kont- vich's famous formula, which solves a long-standing question: How many plane rational curves of degree d pass through 3d -- 1 given points in general position? The formula expresses the number of curves for a given degree in terms of the numbers for lower degrees. A single initial datum is required for the recursion, namely, the case d = I, which simply amounts...