The Resource Knots and primes : an introduction to arithmetic topology, Masanori Morishita, (electronic resource)

Knots and primes : an introduction to arithmetic topology, Masanori Morishita, (electronic resource)

Label
Knots and primes : an introduction to arithmetic topology
Title
Knots and primes
Title remainder
an introduction to arithmetic topology
Statement of responsibility
Masanori Morishita
Creator
Contributor
Provider
Subject
Genre
Language
  • eng
  • jpn
  • eng
Summary
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
Member of
Cataloging source
GW5XE
http://library.link/vocab/creatorDate
1961-
http://library.link/vocab/creatorName
Morishita, Masanori
Image bit depth
0
LC call number
QA611
LC item number
.M6713 2012
Literary form
non fiction
Nature of contents
dictionaries
http://library.link/vocab/relatedWorkOrContributorName
SpringerLink
Series statement
Universitext,
http://library.link/vocab/subjectName
  • Topology
  • Topology
Label
Knots and primes : an introduction to arithmetic topology, Masanori Morishita, (electronic resource)
Instantiates
Publication
Antecedent source
mixed
Bibliography note
Includes bibliographical references (p. 181-187) and index
Color
not applicable
Contents
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
Dimensions
unknown
Extent
1 online resource (xi, 191 p.)
File format
multiple file formats
Form of item
  • online
  • electronic
Isbn
9781447121589
Level of compression
uncompressed
Other physical details
ill.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
  • (OCoLC)765960120
  • (OCoLC)ocn765960120
Label
Knots and primes : an introduction to arithmetic topology, Masanori Morishita, (electronic resource)
Publication
Antecedent source
mixed
Bibliography note
Includes bibliographical references (p. 181-187) and index
Color
not applicable
Contents
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
Dimensions
unknown
Extent
1 online resource (xi, 191 p.)
File format
multiple file formats
Form of item
  • online
  • electronic
Isbn
9781447121589
Level of compression
uncompressed
Other physical details
ill.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
  • (OCoLC)765960120
  • (OCoLC)ocn765960120

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