Knots and primes : an introduction to arithmetic topology / Masanori Morishita.

Format:

Book

Author/Creator:

Morishita, Masanori, 1961-

Series:

Universitext

Universitext, 0172-5939

Standardized Title:

Musubime to sosu. English

Language:

English

Japanese

Subjects (All):

Topology.

Physical Description:

xi, 191 pages : illustrations ; 23 cm.

Place of Publication:

London ; New York : Springer, [2012]

Contents:

1. Introduction

2. Preliminaries

fundamental groups and galois groups

3. Knots and primes, 3-manifolds and number rings

4. Linking numbers and legendre symbols

5. Decompositions of knots and primes

6. Homology groups and ideal class groups I

genus theory

7. Link groups and galois groups with restricted ramification

8. Milnor invariants and multiple residue symbols

9. Alexander modules and Iwasawa modules

10. Homology groups and ideal class groups II

higher order genus theory

11. Homology groups and ideal class groups III

asymptotic formulas

12. Torsions and the Iwasawa main conjecture

13. Moduli spaces of representations of knot and prime groups

14. Deformations of hyperbolic structures and p-Adic ordinary modular forms.

Notes:

"The English language edition is based on the Japanese original edition: Musubime to Sosu by Masanori Morishita copyright Springer Japan 2009"--T.p. verso.

Includes bibliographical references (pages 181-187) and index.

ISBN:

9781447121572

1447121570

OCLC:

775792436