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Graphs on surfaces and their applications

Author: S K Lando; A K Zvonkin
Publisher: Berlin ; New York : Springer, ©2004.
Series: Encyclopaedia of mathematical sciences, v. 141.; Encyclopaedia of mathematical sciences., Low-dimensional topology ;, 2.
Edition/Format:   Print book : EnglishView all editions and formats
Database:WorldCat
Summary:
"Graphs drawn on two-dimensional surfaces have always attracted researchers by their beauty and by the variety of difficult questions to which they give rise. The theory of such embedded graphs, which long seemed rather isolated, has witnessed the appearance of entirely unexpected new applications in recent decades, ranging from Galois theory to quantum gravity models, and has become a kind of a focus of a vast  Read more...
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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: S K Lando; A K Zvonkin
ISBN: 3540002030 9783540002031 9783642055232 3642055230
OCLC Number: 53393734
Description: xv, 455 pages : illustrations ; 25 cm.
Contents: Introduction: What is This Book About --
1. Constellations, Coverings, and Maps --
2. Dessins d'Enfants --
3. Introduction to the Matrix Integrals Method --
4. Geometry of Moduli Spaces of Complex Curves --
5. Meromorphic Functions and Embedded Graphs --
6. Algebraic Structures Associated with Embedded Graphs --
A. Applications of the Representation Theory of Finite Groups / by Don Zagier.
Series Title: Encyclopaedia of mathematical sciences, v. 141.; Encyclopaedia of mathematical sciences., Low-dimensional topology ;, 2.
Other Titles: Grafy na poverkhnosti︠a︡kh i ikh prilozhenii︠a︡.
Responsibility: Sergei K. Lando, Alexander K. Zvonkin ; appendix by Don B. Zagier.
More information:

Abstract:

"Graphs drawn on two-dimensional surfaces have always attracted researchers by their beauty and by the variety of difficult questions to which they give rise. The theory of such embedded graphs, which long seemed rather isolated, has witnessed the appearance of entirely unexpected new applications in recent decades, ranging from Galois theory to quantum gravity models, and has become a kind of a focus of a vast field of research. The book provides an accessible introduction to this new domain, including such topics as coverings of Riemann surfaces, the Galois group action on embedded graphs (Grothendieck's theory of "dessins d'enfants"), the matrix integral method, moduli spaces of curves, the topology of meromorphic functions, and combinatorial aspects of Vassiliev's knot invariants and, in an appendix by Don Zagier, the use of finite group representation theory. The presentation is concrete throughout, with numerous figures, examples (including computer calculations) and exercises, and should appeal to both graduate students and researchers."--Jacket.

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From the reviews: "The goal of this book is to explain the interrelations between three distinct ways to consider an embedded graph: as a topological object, as a sequence of permutations, as a way Read more...

 
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