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Sinopsis
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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De la contraportada
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. Common aspects of both knot theory and number theory, for instance knots in three manifolds versus primes in a number field, are compared throughout the book. These comparisons begin at an elementary level, slowly building up to advanced theories in later chapters. Definitions are carefully formulated and proofs are largely self-contained.
When necessary, background information is provided and theory is accompanied with a number of useful examples and illustrations, making this a useful text for both undergraduates and graduates in the field of knot theory, number theory and geometry.
"Sobre este título" puede pertenecer a otra edición de este libro.
- EditorialSpringer
- Año de publicación2011
- ISBN 10 1447121570
- ISBN 13 9781447121572
- EncuadernaciónTapa blanda
- IdiomaInglés
- Número de páginas204
- Contacto del fabricanteno disponible
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Knots and Primes
Librería: Agapea Libros, Malaga, MA, España
Calificación del vendedor: 5 de 5 estrellas
Condición: New. Idioma/Language: Inglés. 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. Common aspects of both knot theory and number theory, for instance knots in three manifolds versus primes in a number field, are compared throughout the book. These comparisons begin at an elementary level, slowly building up to advanced theories in later chapters. Definitions are carefully formulated and proofs are largely self-contained. When necessary, background information is provided and theory is accompanied with a number of useful examples and illustrations, making this a useful text for both undergraduates and graduates in the field of knot theory, number theory and geometry. ? *** Nota: Los envíos a España peninsular, Baleares y Canarias se realizan a través de mensajería urgente. No aceptamos pedidos con destino a Ceuta y Melilla. Nº de ref. del artículo: 6595843
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