Knots and primes : an introduction to arithmetic topology / Masanori Morishita.
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...
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| Online Access: |
Full Text (via Springer) |
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| Main Author: | |
| Format: | eBook |
| Language: | English |
| Published: |
Singapore :
Springer,
[2024]
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| Edition: | Second edition. |
| Series: | Universitext.
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| Subjects: |
| Summary: | 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 tale 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 DijkgraafWitten theory, which supports a new bridge between arithmetic topology and mathematical physics. |
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| Physical Description: | 1 online resource (xv, 259 pages) : illustrations. |
| ISBN: | 9789819992553 9819992559 |
| Source of Description, Etc. Note: | Description based on online resource; title from digital title page (viewed on June 25, 2024). |