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Graphs on Surfaces and Their Applications

  • Sergei K. Lando
  • Alexander K. Zvonkin

Part of the Encyclopaedia of Mathematical Sciences book series (EMS, volume 141)

Table of contents

  1. Front Matter
    Pages I-XV
  2. Sergei K. Lando, Alexander K. Zvonkin
    Pages 1-5
  3. Sergei K. Lando, Alexander K. Zvonkin
    Pages 7-77
  4. Sergei K. Lando, Alexander K. Zvonkin
    Pages 79-153
  5. Sergei K. Lando, Alexander K. Zvonkin
    Pages 155-221
  6. Sergei K. Lando, Alexander K. Zvonkin
    Pages 223-268
  7. Sergei K. Lando, Alexander K. Zvonkin
    Pages 269-336
  8. Sergei K. Lando, Alexander K. Zvonkin
    Pages 337-397
  9. Back Matter
    Pages 399-455

About this book

Introduction

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.

Keywords

Algebraic structure Galois theory Group representation Knot invariant Meromorphic function Representation theory Riemann surfaces Vassiliev invariants algebra embedded graphs graphs matrix integrals moduli of curves

Authors and affiliations

  • Sergei K. Lando
    • 1
  • Alexander K. Zvonkin
    • 2
  1. 1.Higher College of Mathematics, Institute for System Research, Russian Academy of SciencesIndependent University of MoscowMoscowRussia
  2. 2.LaBRIUniversité Bordeaux ITalence CedexFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-540-38361-1
  • Copyright Information Springer-Verlag Berlin Heidelberg 2004
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-05523-2
  • Online ISBN 978-3-540-38361-1
  • Series Print ISSN 0938-0396
  • Buy this book on publisher's site