| 书目名称 | Knots and Primes | | 副标题 | An Introduction to A | | 编辑 | Masanori Morishita | | 视频video | http://file.papertrans.cn/544/543791/543791.mp4 | | 概述 | Is the new, updated edition of the first book on arithmetic topology.Provides a solid foundation of arithmetic topology for graduate students and researchers.Includes useful problems guiding future st | | 丛书名称 | Universitext | | 图书封面 |  | | 描述 | This book provides a foundation for arithmetic topology, a new branch of mathematics that investigates the analogies between the topology of knots, 3-manifolds, and the arithmetic of number fields. Arithmetic topology is now becoming a powerful guiding principle and driving force to obtain parallel results and new insights between 3-dimensional geometry and number theory..After an informative introduction to Gauss‘ work, in which arithmetic topology originated, the text reviews a background from both topology and number theory. The analogy between knots in 3-manifolds and primes in number rings, the founding principle of the subject, is based on the étale topological interpretation of primes and number rings. On the basis of this principle, the text explores systematically intimate analogies and parallel results of various concepts and theories between 3-dimensional topology and number theory. The presentation of these analogies begins at an elementary level, gradually building to advanced theories in later chapters. Many results presented here are new and original..References are clearly provided if necessary, and many examples and illustrations are included. Some useful problems | | 出版日期 | Textbook 2024Latest edition | | 关键词 | 3-manifolds; arithmetic topology; homology groups; knots and primes; legendre symbols; number rings | | 版次 | 2 | | doi | https://doi.org/10.1007/978-981-99-9255-3 | | isbn_softcover | 978-981-99-9254-6 | | isbn_ebook | 978-981-99-9255-3Series ISSN 0172-5939 Series E-ISSN 2191-6675 | | issn_series | 0172-5939 | | copyright | The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapor |
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