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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)
Resource Information
The item Knots and primes : an introduction to arithmetic topology, Masanori Morishita, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Boston University Libraries.This item is available to borrow from all library branches.
Resource Information
The item Knots and primes : an introduction to arithmetic topology, Masanori Morishita, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Boston University Libraries.
This item is available to borrow from all library branches.
 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 selfcontained. 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
 Language

 eng
 jpn
 eng
 Extent
 1 online resource (xi, 191 p.)
 Contents

 Preliminaries  Fundamental Groups and Galois Groups
 Knots and Primes, 3Manifolds 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 padic Ordinary Modular Forms
 Isbn
 9781447121589
 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
 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 selfcontained. 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
 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)
 Antecedent source
 mixed
 Bibliography note
 Includes bibliographical references (p. 181187) and index
 Color
 not applicable
 Contents
 Preliminaries  Fundamental Groups and Galois Groups  Knots and Primes, 3Manifolds 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 padic 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)
 Antecedent source
 mixed
 Bibliography note
 Includes bibliographical references (p. 181187) and index
 Color
 not applicable
 Contents
 Preliminaries  Fundamental Groups and Galois Groups  Knots and Primes, 3Manifolds 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 padic 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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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.bu.edu/portal/Knotsandprimesanintroductiontoarithmetic/jzP7KmAEZYw/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.bu.edu/portal/Knotsandprimesanintroductiontoarithmetic/jzP7KmAEZYw/">Knots and primes : an introduction to arithmetic topology, Masanori Morishita, (electronic resource)</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.bu.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.bu.edu/">Boston University Libraries</a></span></span></span></span></div>