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The Resource Quandles and topological pairs : symmetry, knots, and cohomology, Takefumi Nosaka, (electronic book)

Quandles and topological pairs : symmetry, knots, and cohomology, Takefumi Nosaka, (electronic book)

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Author
Summary
This book surveys quandle theory, starting from basic motivations and going on to introduce recent developments of quandles with topological applications and related topics. The book is written from topological aspects, but it illustrates how esteemed quandle theory is in mathematics, and it constitutes a crash course for studying quandles. More precisely, this work emphasizes the fresh perspective that quandle theory can be useful for the study of low-dimensional topology (e.g., knot theory) and relative objects with symmetry. The direction of research is summarized as zWe shall thoroughly (re)interpret the previous studies of relative symmetry in terms of the quandley. The perspectives contained herein can be summarized by the following topics. The first is on relative objects G/H, where G and H are groups, e.g., polyhedrons, reflection, and symmetric spaces. Next, central extensions of groups are discussed, e.g., spin structures, K2 groups, and some geometric anomalies. The third topic is a method to study relative information on a 3-dimensional manifold with a boundary, e.g., knot theory, relative cup products, and relative group cohomology. For applications in topology, it is shown that from the perspective that some existing results in topology can be recovered from some quandles, a method is provided to diagrammatically compute some zrelative homologyy. (Such classes since have been considered to be uncomputable and speculative). Furthermore, the book provides a perspective that unifies some previous studies of quandles. The former part of the book explains motivations for studying quandles and discusses basic properties of quandles. The latter focuses on low-dimensional topology or knot theory. Finally, problems and possibilities for future developments of quandle theory are posed.--
Language
eng
Work
Publication
Extent
1 online resource.
Isbn
9789811067921
Instance
Label
Quandles and topological pairs : symmetry, knots, and cohomology
Title
Quandles and topological pairs
Title remainder
symmetry, knots, and cohomology
Statement of responsibility
Takefumi Nosaka
Creator
Author
Subject
Language
eng
Summary
This book surveys quandle theory, starting from basic motivations and going on to introduce recent developments of quandles with topological applications and related topics. The book is written from topological aspects, but it illustrates how esteemed quandle theory is in mathematics, and it constitutes a crash course for studying quandles. More precisely, this work emphasizes the fresh perspective that quandle theory can be useful for the study of low-dimensional topology (e.g., knot theory) and relative objects with symmetry. The direction of research is summarized as zWe shall thoroughly (re)interpret the previous studies of relative symmetry in terms of the quandley. The perspectives contained herein can be summarized by the following topics. The first is on relative objects G/H, where G and H are groups, e.g., polyhedrons, reflection, and symmetric spaces. Next, central extensions of groups are discussed, e.g., spin structures, K2 groups, and some geometric anomalies. The third topic is a method to study relative information on a 3-dimensional manifold with a boundary, e.g., knot theory, relative cup products, and relative group cohomology. For applications in topology, it is shown that from the perspective that some existing results in topology can be recovered from some quandles, a method is provided to diagrammatically compute some zrelative homologyy. (Such classes since have been considered to be uncomputable and speculative). Furthermore, the book provides a perspective that unifies some previous studies of quandles. The former part of the book explains motivations for studying quandles and discusses basic properties of quandles. The latter focuses on low-dimensional topology or knot theory. Finally, problems and possibilities for future developments of quandle theory are posed.--
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Cataloging source
YDX
http://library.link/vocab/creatorName
Nosaka, Takefumi
Dewey number
514/.2242
Index
no index present
LC call number
QA612.2
Literary form
non fiction
Nature of contents
dictionaries
Series statement
Springer briefs in mathematics
http://library.link/vocab/subjectName
  • Knot theory
  • Low-dimensional topology
Label
Quandles and topological pairs : symmetry, knots, and cohomology, Takefumi Nosaka, (electronic book)
Instantiates
Publication
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Dimensions
unknown
Extent
1 online resource.
Form of item
online
Isbn
9789811067921
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Specific material designation
remote
System control number
  • (OCoLC)1013174825
  • on1013174825
Label
Quandles and topological pairs : symmetry, knots, and cohomology, Takefumi Nosaka, (electronic book)
Publication
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Dimensions
unknown
Extent
1 online resource.
Form of item
online
Isbn
9789811067921
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Specific material designation
remote
System control number
  • (OCoLC)1013174825
  • on1013174825

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