Graphs on Surfaces and Their Applications

Sergei K. Lando, Alexander K. Zvonkin

456 pages, parution le 11/12/2003

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Résumé

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.

Written for:
Graduate students and researchers

Introduction: What is This Book About
Constellations, Coverings, and Maps
Dessins d'Enfants
Introduction to the Matrix Integrals Method
Geometry of Moduli Spaces of Complex Curves
Meromorphic Functions and Embedded Graphs
Algebraic Structures Associated with Embedded Graphs
A Applications of the Representation Theory of Finite Groups (by Don Zagier)
References
Index

Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Sergei K. Lando, Alexander K. Zvonkin
Parution	11/12/2003
Nb. de pages	456
Format	16 x 24
Couverture	Relié
Poids	820g
Intérieur	Noir et Blanc
EAN13	9783540002031