Graphs on surfaces and their applications
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Contributions
- Zvonkin, Alexander K - Contributor
- Zagier, Don, 1951- - Contributor
Publication
2003 - Springer, Berlin
Language
English
Word Count
113,750 words, Guess
Page Count
455 pages
Identifiers
- Open LibraryOL17117237M
- ISBN-103540002030
- OCLC Control Number53393734
- OCLC Control Numberlowdimensionalto00land
- Library of Congress Control Number2004298443
and 1 more
- Goodreads183777
Classifications
- LCCQA166 .L36 2004
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.
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."--BOOK JACKET.
Subjects
Topics
Series Statement
- Encyclopaedia of mathematical sciences -- v. 141. -- Low-dimensional topology -- 2
Other Editions
- Graphs on surfaces and their applications
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