Cover Image
Read Now

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...

Full description

Bibliographic Details
Main Author: Morishita, Masanori
Format: eBook
Language:English
Published: Singapore Springer Nature Singapore 2024, 2024
Edition:2nd ed. 2024
Series:Universitext
Subjects:
Number Theory
Topology
Mathematics
Online Access:
Collection: Springer eBooks 2005- - Collection details see MPG.ReNa
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

Similar Items