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.

Reviews

“This is one of the best textbook I have seen in the last few years. … this books is amazing! I really enjoyed it and I hope you will also enjoy it. It definitely should be part of your library if you work in number theory and/or topology. This book will become a classical very soon!” (Philosophy, Religion and Science Book Reviews, bookinspections.wordpress.com, June, 2016)“The book under review is the first systematic treatment of the subject in a format suitable for a textbook. … The book is rich in material for anybody interested in either the arithmetic or the topological side, and the connections and interactions are presented in a very convincing and detailed way.” (Matilde Marcolli, Mathematical Reviews, March, 2013)“Once you’ve lived long enough in mathematics, the themes addressed in Knots and Primes: An Introduction to Arithmetic Topology are both familiar and exceedingly attractive. This is a fascinating topic … and Morishita’s book is an important contribution. … it will spur a lot of work in this beatiful and accessible area of contemporary mathematics.” (Michael Berg, The Mathematical Association of America, May, 2012)