Overview
- 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 study for graduate students and researchers
Part of the book series: Universitext (UTX)
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Table of contents (16 chapters)
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Front Matter
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Back Matter
Keywords
About this book
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 are also given for future research. All these components make the book useful for graduate students and researchers in number theory, low dimensional topology, and geometry.
This second edition is a corrected and enlarged version of the original one. Misprints and mistakes in the first edition are corrected, references are updated, and some expositions are improved. Because of the remarkable developments in arithmetic topology after the publication of the first edition, the present edition includes two new chapters. One is concerned with idelic class field theory for 3-manifolds and number fields. The other deals with topological and arithmetic Dijkgraaf–Witten theory, which supports a new bridge between arithmetic topology and mathematical physics.
Authors and Affiliations
About the author
The author is currently Professor at Kyushu University. He previously held positions at Kanazawa University.
Bibliographic Information
Book Title: Knots and Primes
Book Subtitle: An Introduction to Arithmetic Topology
Authors: Masanori Morishita
Series Title: Universitext
DOI: https://doi.org/10.1007/978-981-99-9255-3
Publisher: Springer Singapore
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024
Softcover ISBN: 978-981-99-9254-6Published: 28 May 2024
eBook ISBN: 978-981-99-9255-3Published: 27 May 2024
Series ISSN: 0172-5939
Series E-ISSN: 2191-6675
Edition Number: 2
Number of Pages: XV, 259
Number of Illustrations: 78 b/w illustrations
Topics: Number Theory, Topology, Mathematics, general