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＜電子ブック＞
Graphs on Surfaces and Their Applications / by Sergei K. Lando, Alexander K. Zvonkin ; edited by R.V. Gamkrelidze, V.A. Vassiliev
(Encyclopaedia of Mathematical Sciences ; 141)

版	1st ed. 2004.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	2004
本文言語	英語
大きさ	XV, 455 p. 3 illus : online resource
著者標目	*Lando, Sergei K author Zvonkin, Alexander K author Gamkrelidze, R.V editor Vassiliev, V.A editor SpringerLink (Online service)
件　名	LCSH:Topology LCSH:Discrete mathematics LCSH:Algebraic geometry LCSH:Functions of complex variables LCSH:Mathematical physics LCSH:Algorithms FREE:Topology FREE:Discrete Mathematics FREE:Algebraic Geometry FREE:Several Complex Variables and Analytic Spaces FREE:Theoretical, Mathematical and Computational Physics FREE:Algorithms
一般注記	0 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.1 Representation Theory of Finite Groups -- A.1.1 Irreducible Representations and Characters -- A.1.2 Examples -- A.1.3 Frobenius’s Formula -- A.2 Applications -- A.2.2 Examples -- A.2.3 First Application: Enumeration of Polygon Gluings -- A.2.4 Second Application: the Goulden-Jackson Formula -- A.2.5 Third Application: “Mirror Symmetry” in Dimension One -- References 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 HTTP:URL=https://doi.org/10.1007/978-3-540-38361-1

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