Graphs on Surfaces and Their Applications
Graphs on Surfaces and Their Applications
复制标题
DOI：
10.1007/978-3-540-38361-1
复制
发表时间：
2003-12
期刊：
影响因子：
--
通讯作者：
S. Lando;A. Zvonkin
中科院分区：
文献类型：
--
作者：
S. Lando;A. Zvonkin
在二维表面上绘制的图形总是以其美丽和它们所引起的各种困难问题吸引着研究人员。这种嵌入图的理论，长期以来似乎是相当孤立的，在最近几十年里已经见证了完全意想不到的新应用的出现，从伽罗瓦理论到量子引力模型，并已成为一个广泛的研究领域的一个焦点。这本书提供了一个方便的介绍这一新的领域，包括这样的主题覆盖黎曼曲面，伽罗瓦集团行动嵌入图（Grothendieck的理论”dessins d 'enfants”），矩阵积分方法，模空间的曲线，拓扑的亚纯函数，和组合方面的瓦西里耶夫结不变量，并在附录由唐Zagier，使用有限群表示理论。整个演示文稿是具体的，有许多数字，例子（包括计算机计算）和练习，并应呼吁研究生和研究人员。
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.