Introduction: What is This Book About
The theory of maps (sometimes also called embedded graphs, or ribbon graphs, or fat graphs, or graphs with rotation), or, otherwise, the topological graph theory, is an old and well established branch of combinatorics. It may justifiably be proud of such classical results as the Euler formula (relating the number of vertices, edges, and faces of a map with the genus of the corresponding surface), and of such notably difficult modern achievements as the Four Color Theorem. But the last two decades witnessed a kind of a volcanic activity in this domain which would have been difficult to predict some 30 years ago.
KeywordsModulus Space Riemann Surface Meromorphic Function Hopf Algebra Galois Theory
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