Knots and Primes An Introduction to Arithmetic Topology /

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...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Morishita, Masanori (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: London : Springer London : Imprint: Springer, 2012.
Edición:1st ed. 2012.
Colección:Universitext,
Temas:
Number theory.
Topology.
Mathematics.
Number Theory.
Acceso en línea:Texto Completo
Tabla de Contenidos:
  • 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.

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