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

MARC

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245 1 0 |a Knots and Primes  |h [electronic resource] :  |b An Introduction to Arithmetic Topology /  |c by Masanori Morishita. 
250 |a 1st ed. 2012. 
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300 |a XI, 191 p. 42 illus.  |b online resource. 
336 |a text  |b txt  |2 rdacontent 
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490 1 |a Universitext,  |x 2191-6675 
505 0 |a 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. 
520 |a 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. 
650 0 |a Number theory. 
650 0 |a Topology. 
650 0 |a Mathematics. 
650 1 4 |a Number Theory. 
650 2 4 |a Topology. 
650 2 4 |a Mathematics. 
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773 0 |t Springer Nature eBook 
776 0 8 |i Printed edition:  |z 9781447121572 
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830 0 |a Universitext,  |x 2191-6675 
856 4 0 |u https://doi.uam.elogim.com/10.1007/978-1-4471-2158-9  |z Texto Completo 
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950 |a Mathematics and Statistics (SpringerNature-11649) 
950 |a Mathematics and Statistics (R0) (SpringerNature-43713) 

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