Hyperbolic Manifolds and Discrete Groups pdf epub mobi txt 电子书下载 2026

简体网页||繁体网页

☆☆☆☆☆

出版者:Birkhäuser Boston

作者:Michael Kapovich

出品人:

页数:492

译者:

出版时间:2000-11-03

价格:USD 119.00

装帧:Hardcover

isbn号码:9780817639044

丛书系列:

图书标签:

美国
数学
Mathematics
Hyperbolic geometry
Manifolds
Discrete groups
Topology
Geometric group theory
Kleinian groups
Hyperbolic 3-manifolds
Teichmüller theory
Low-dimensional topology
Representation theory

下载链接在页面底部

facebook linkedin mastodon messenger pinterest reddit telegram twitter viber vkontakte whatsapp 复制链接

想要找书就要到小哈图书下载中心

qciss.net

立刻按 ctrl+D收藏本页

你会得到大惊喜!!

具体描述

"Hyperbolic Manifolds and Discrete Groups" is at the crossroads of several branches of mathematics: hyperbolic geometry, discrete groups, 3-dimensional topology, geometric group theory, and complex analysis. The main focus throughout is on the 'Big Monster', i.e., on Thurston's hyperbolization theorem, which has not only completely changed the landscape of 3-dimensional topology and Kleinian group theory but is one of the central results of 3-dimensional topology. The book presents the first complete proof of Thurston's hyperbolization theorem in the 'generic case' and an outline of Otal's proof of the hyperbolization theorem for manifolds fibered over the circle. This important work contains an extended treatment of the theory of Kleinian groups and group actions on trees, including such key topics as: the Kazhdan-Margulis-Zassenhaus theorem; the Klein and Maskit combination theorems; the Mostow rigidity theorem; the Douady-Earle extension theorem for homeomorphisms of the circle; the smoothness theorem for representation varieties of Kleinian groups; the Ahlfors finiteness theorem; the Brooks deformation theorem; characterization of pseudo-Anosov homeomorphisms; and, compactification of character varieties via group actions on trees.

《Hyperbolic Manifolds and Discrete Groups》是一本深入浅出的学术著作，专注于探讨几何与群论之间的交汇点。这本书系统地介绍了双曲几何这一重要的数学概念，并通过详尽的理论解释和丰富的例子，帮助读者理解其在现代数学研究中的重要性。书中首先深入分析了双曲空间的基本结构，从拓扑特征到代数化建模，无不体现出对纯数学思维的深刻把握。通过严谨的推导与清晰的解释，读者不仅能掌握相关概念，还能够看到这些理论在实际应用中的广泛潜力。同时，书中同样细致地阐述了离散群理论这一核心内容，揭示其在数学结构、对称性分析以及计算几何等领域的深远影响。这部分章节通过多层次的逻辑展开，帮助读者理解复杂抽象概念的内涵，同时结合经典案例，展示这些理论如何构建数学家的思路与研究框架。书中注重平衡理论与应用之间的关系，为前沿课题提供了有力的支持和参考依据。此外，该书还融入了大量图示和实例，使复杂的几何结构变得更加直观易懂。通过详细描述双曲形态的几何属性及其分类，读者可以更深刻地领会数学建模中不同理论的相互作用。书中的内容设计思路清晰，层次分明，不仅适合对该领域有深入兴趣的研究者，也为初学者提供了良好的学习起点。这本书通过严谨的论述和精细的分析，系统地呈现了双曲几何与离散群理论之间复杂而精妙的联系，为读者打开了一扇深入探索数学奥义的大门。无论是数学专业的学子，还是对这一主题有兴趣的爱好者，都可以从中获得丰富的知识和启发。这是一部兼具理论深度与实践指导的优秀学术著作，值得每一位读者认真研读。总体而言，《Hyperbolic Manifolds and Discrete Groups》不仅传递着对数学本质的深刻理解，更在其中为读者搭建了通往更高层次数学思维的桥梁。这是一部经典之作，将理论与实际相结合，为后续研究提供坚实基础。通过这本书，读者将能够更全面地认识这一领域的重要内容和应用价值，从而拓展其学术视野。