Graphs on surfaces and their applications

Author(s)

Bibliographic Information

Graphs on surfaces and their applications

Sergei K. Lando, Alexander K. Zvonkin ; appendix by Don B. Zagier

(Encyclopaedia of mathematical sciences / editor-in-chief, R.V. Gamkrelidze, v. 141 . Low-dimensional topology ; 2)

Springer, c2004

  • : softcover

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Note

Bibliography: p. [429]-444

Includes index

Description and Table of Contents

Description

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.

Table of Contents

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.

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Details

  • NCID
    BA64843568
  • ISBN
    • 3540002030
    • 9783642055232
  • Country Code
    gw
  • Title Language Code
    eng
  • Text Language Code
    eng
  • Place of Publication
    Berlin ; Tokyo
  • Pages/Volumes
    xv, 455 p.
  • Size
    25 cm
  • Classification
  • Subject Headings
  • Parent Bibliography ID
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