Knots and Primes

The author is currently Professor at Kyushu University. He previously held positions at Kanazawa University.

• 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.