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Knots and Primes An Introduction to Arithmetic Topology /

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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Bibliographic Details
Main Author: Morishita, Masanori (Author)
Corporate Author: SpringerLink (Online service)
Format: Electronic eBook
Language:English
Published: Singapore : Springer Nature Singapore : Imprint: Springer, 2024.
Edition:2nd ed. 2024.
Series:Universitext,
Subjects:
Number theory.
Topology.
Mathematics.
Number Theory.
Online Access:https://doi.org/10.1007/978-981-99-9255-3
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Table of Contents:
  • Chapter 1. Introduction
  • Chapter 2. Preliminaries - Fundamental Groups and Galois Groups.-Chapter 3. Knots and Primes, 3-Manifolds and Number Rings
  • Chapter 4. Linking Numbers and Legendre Symbols
  • Chapter 5. Decompositions of Knots and Primes
  • Chapter 6. Homology Groups and Ideal Class Groups I – Genus Theory
  • Chapter 7. Idelic Class Field Theory for 3-Manifolds and Number Fields
  • Chapter 8. Link Groups and Galois Groups with Restricted Ramification
  • Chapter 9. Milnor Invariants and Multiple Power Residue Symbols
  • Chapter 10. Alexander Modules and Iwasawa Modules
  • Chapter 11. Homology Groups and Ideal Class Groups II – Higher Order Genus Theory
  • Chapter 12. Homology Groups and Ideal Class Groups III – Asymptotic Formulas
  • Chapter 13. Torsions and the Iwasawa Main Conjecture
  • Chapter 14. Moduli Spaces of Representations of Knot and Prime Groups
  • Chapter 15. Deformations of Hyperbolic Structures and of p-Adic Ordinary Modular Forms
  • Chapter 16. Dijkgraaf–Witten Theory for 3-Manifolds and Number Rings.

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