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## Details

Material Type: | Internet resource |
---|---|

Document Type: | Book, Internet Resource |

All Authors / Contributors: |
S K Lando; A K Zvonkin |

ISBN: | 3540002030 9783540002031 |

OCLC Number: | 53393734 |

Description: | xv, 455 pages : illustrations ; 25 cm. |

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. |

Series Title: | Encyclopaedia of mathematical sciences, v. 141.; Encyclopaedia of mathematical sciences., Low-dimensional topology ;, 2. |

Other Titles: | Grafy na poverkhnosti︠a︡kh i ikh prilozhenii︠a︡. |

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

More information: |

## Reviews

*Editorial reviews*

Publisher Synopsis

From the reviews: "The goal of this book is to explain the interrelations between three distinct ways to consider an embedded graph: as a topological object, as a sequence of permutations, as a way of representing a ramified covering of the sphere by a compact two-dimensional manifold. ... The authors introduce their objects of study, namely graphs and maps, with great care and detail. A wealth of applications is pointed out, but of course these applications are sometimes introduced with minimal or no explanation. The Appendix provides some elegant and concise proofs of results used in the main body of the book and the bibliography contains 313 entries. Well-chosen examples and strategically placed exercises support the reader in gaining an understanding of graphs on surfaces and their fascinating applications." B.Servatius, Zentralblatt fur Math. 1040, Issue 9, p. 11, 2004 "This fascinating book is concerned with a modern approach to topological graph theory, with a particular focus on the numerous unexpected applications to, and interrelationships with, other fields of mathematics and also quantum physics, guiding the reader to the cutting edge of current research. ... The book ends with a useful crash course on the representation theory of finite groups and their relevance to the enumeration of constellations, in the form of an appendix written by Don Zagier. The book contains numerous diagrams, examples and exercises, making it appealing to both students and researchers." Mathai Varghese, The Australian Mathematical Gazette, Vol. 31, Number 4, September 2004 "The goal of this book is to explain the interrelations between three distinct ways to consider an embedded graph ... . The authors introduce their objects of study ... with great care and detail. A wealth of applications is pointed out ... . The Appendix provides some elegant and concise proofs of results used in the main body of the book ... . Well-chosen examples and strategically placed exercises support the reader in gaining an understanding of graphs on surfaces and their fascinating applications." (Brigitte Servatius, Zentralblatt MATH, Vol. 1040 (9), 2004) "This fascinating book is concerned with a modern approach to topological graph theory ... guiding the reader to the cutting edge of current research. ... The book ends with a useful crash course on the representation theory of finite groups and their relevance to the enumeration of constellations, in the form of an appendix written by Don Zagier. The book contains numerous diagrams, examples and exercises, making it appealing to both students and researchers." (Mathai Varghese, The Australian Mathematical Society Gazette, Vol. 31 (4), 2004) "The book by Sergei Lando and Alexander Zvonkin is a pleasant new surprise. It brings some fresh air into the subject. ... it shows a great variety of applications, some from the 'mainstream' of mathematics, where embedded graphs can be used, and have been used, to get enhanced results, simplified proofs and deeper understanding. ... I dare to predict that this book will have some serious impact on the future development of topological graph theory." (Bojan Mohar, Combinatorics, Probability and Computing, Vol. 15, 2006) "The nature of this fascinating book is well captured by the story of its origin. Several Russian mathematicians were talking about the topics they had chosen to use with the high school students in their Math Circles. ... The book is charmingly written. ... The overall effect is to draw the reader in and to open up a wide vista of little-known mathematics that is full of surprising ideas, unexpected connections, and just-plain-wonderful theorems. This is a tour worth taking." (Fernando Q. Gouvea, The Mathematical Association of America, June, 2010) Read more...

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