Format:
Online-Ressource
,
v.: digital
Edition:
Online-Ausg. Springer eBook Collection. Mathematics and Statistics Electronic reproduction; Available via World Wide Web
ISBN:
9781447121589
Series Statement:
Universitext
Note:
"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 (p. 181-187) and index
,
""Knots and Primes""; ""Preface""; ""Contents""; ""Notation and Convention""; ""Chapter 1: Introduction""; ""1.1 Two Ways that Branched out from C.F. Gauss-Quadratic Residues and Linking Numbers""; ""1.2 Geometrization of Number Theory""; ""1.3 The Outline of This Book""; ""Chapter 2: Preliminaries-Fundamental Groups and Galois Groups""; ""2.1 The Case of Topological Spaces""; ""2.2 The Case of Arithmetic Rings""; ""2.3 Class Field Theory""; ""2.3.1 Finite Fields""; ""2.3.2 p-Adic Fields""; ""2.3.3 Number Rings""; ""Chapter 3: Knots and Primes, 3-Manifolds and Number Rings""
,
""Chapter 4: Linking Numbers and Legendre Symbols""""4.1 Linking Numbers""; ""4.2 Legendre Symbols""; ""Summary""; ""Chapter 5: Decompositions of Knots and Primes""; ""5.1 Decomposition of a Knot""; ""5.2 Decomposition of a Prime""; ""Summary""; ""Chapter 6: Homology Groups and Ideal Class Groups I-Genus Theory""; ""6.1 Homology Groups and Ideal Class Groups""; ""Hurewicz Theorem""; ""Artin Reciprocity""; ""6.2 Genus Theory for a Link""; ""6.3 Genus Theory for Prime Numbers""; ""Summary""; ""Chapter 7: Link Groups and Galois Groups with Restricted Rami cation""; ""7.1 Link Groups""
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""7.2 Pro-l Galois Groups with Restricted Rami cation""""Summary""; ""Chapter 8: Milnor Invariants and Multiple Residue Symbols""; ""8.1 Fox Free Differential Calculus""; ""8.2 Milnor Invariants""; ""8.3 Pro-l Fox Free Differential Calculus""; ""8.4 Multiple Residue Symbols""; ""Summary""; ""Chapter 9: Alexander Modules and Iwasawa Modules""; ""9.1 Differential Modules""; ""9.2 The Crowell Exact Sequence""; ""9.3 Complete Differential Modules""; ""9.4 The Complete Crowell Exact Sequence""; ""Summary""; ""Chapter 10: Homology Groups and Ideal Class Groups II-Higher Order Genus Theory""
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""10.1 The Universal Linking Matrix for a Link""""10.2 Higher Order Genus Theory for a Link""; ""10.3 The Universal Linking Matrix for Primes""; ""10.4 Higher Order Genus Theory for Primes""; ""Summary""; ""Chapter 11: Homology Groups and Ideal Class Groups III-Asymptotic Formulas""; ""11.1 The Alexander Polynomial and Homology Groups""; ""11.2 The Iwasawa Polynomial and p-Ideal Class Groups""; ""Summary""; ""Chapter 12: Torsions and the Iwasawa Main Conjecture""; ""12.1 Torsions and Zeta Functions""; ""12.2 The Iwasawa Main Conjecture""; ""Summary""
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""Chapter 13: Moduli Spaces of Representations of Knot and Prime Groups""""13.1 Character Varieties of Complex Representations of a Knot Group""; ""13.2 The Character Variety of Complex 1-Dimensional Representations of a Knot Group and Alexander Ideals""; ""13.3 Universal Deformation Spaces of p-Adic Representations of a Prime Group""; ""13.4 The Universal Deformation Space of p-Adic 1-Dimensional Representations of a Prime Group and Iwasawa Ideals""; ""Summary""; ""Chapter 14: Deformations of Hyperbolic Structures and p-Adic Ordinary Modular Forms""
,
""14.1 Deformation of Hyperbolic Structures""
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Electronic reproduction; Available via World Wide Web
Additional Edition:
ISBN 9781447121572
Additional Edition:
Erscheint auch als Druck-Ausgabe Morishita, Masanori, 1961 - Knots and primes London [u.a.] : Springer, 2012 ISBN 9781447121572
Language:
English
Subjects:
Mathematics
Keywords:
Knotentheorie
;
Zahlentheorie
DOI:
10.1007/978-1-4471-2158-9
URL:
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