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)
Resource Information
The item Quandles and topological pairs : symmetry, knots, and cohomology, Takefumi Nosaka, (electronic book) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Liverpool.This item is available to borrow from 1 library branch.
Resource Information
The item Quandles and topological pairs : symmetry, knots, and cohomology, Takefumi Nosaka, (electronic book) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Liverpool.
This item is available to borrow from 1 library branch.
 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 lowdimensional 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 3dimensional 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 lowdimensional topology or knot theory. Finally, problems and possibilities for future developments of quandle theory are posed.
 Language
 eng
 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
 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 lowdimensional 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 3dimensional 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 lowdimensional topology or knot theory. Finally, problems and possibilities for future developments of quandle theory are posed.
 Assigning source
 Provided by publisher
 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
 Lowdimensional topology
 Label
 Quandles and topological pairs : symmetry, knots, and cohomology, Takefumi Nosaka, (electronic book)
 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)
 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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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.liverpool.ac.uk/portal/Quandlesandtopologicalpairssymmetryknots/sB1oVxFdFkU/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.liverpool.ac.uk/portal/Quandlesandtopologicalpairssymmetryknots/sB1oVxFdFkU/">Quandles and topological pairs : symmetry, knots, and cohomology, Takefumi Nosaka, (electronic book)</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.liverpool.ac.uk/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.liverpool.ac.uk/">University of Liverpool</a></span></span></span></span></div>