Graphs on surfaces and their applications

著者

書誌事項

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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注記

Bibliography: p. [429]-444

Includes index

内容説明・目次

内容説明

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.

目次

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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詳細情報

  • NII書誌ID(NCID)
    BA64843568
  • ISBN
    • 3540002030
    • 9783642055232
  • 出版国コード
    gw
  • タイトル言語コード
    eng
  • 本文言語コード
    eng
  • 出版地
    Berlin ; Tokyo
  • ページ数/冊数
    xv, 455 p.
  • 大きさ
    25 cm
  • 分類
  • 件名
  • 親書誌ID
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