Descuento:
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Despues:
51,33 €- Starts at an elementary level and builds up to a more advanced
theoretical discussion
- Written by a world expert on arithmetic topology
- A large number of illustrative examples are provided throughout
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.
Table of contents (14 chapters)
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
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