Knots and Primes An Introduction to Arithmetic Topology /

• Main Author: Morishita, Masanori (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: London : Springer London, 2012.
• Series: Universitext,
• Subjects: Mathematics.; Number theory.; Topology.; Number Theory.; Mathematics, general.

This is a foundation for arithmetic topology - a new branch of mathematics which is focused upon the analogy between knot theory and number theory.  Starting with an informative introduction to its origins, namely Gauss, this text provides a background on knots, three manifolds and number fields. Co...

Table of Contents:

• Preliminaries - Fundamental Groups and Galois Groups
• Knots and Primes, 3-Manifolds and Number Rings
• Linking Numbers and Legendre Symbols
• Decompositions of Knots and Primes
• Homology Groups and Ideal Class Groups I - Genus Theory
• Link Groups and Galois Groups with Restricted Ramification
• Milnor Invariants and Multiple Power Residue Symbols
• Alexander Modules and Iwasawa Modules
• Homology Groups and Ideal Class Groups II - Higher Order Genus Theory
• Homology Groups and Ideal Class Groups III - Asymptotic Formulas
• Torsions and the Iwasawa Main Conjecture
• Moduli Spaces of Representations of Knot and Prime Groups
• Deformations of Hyperbolic Structures and of p-adic Ordinary Modular Forms.