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dc.contributor.author
Clark, W. Edwin
dc.contributor.author
Saito, Masahico
dc.contributor.author
Vendramin, Claudio Leandro
dc.date.available
2018-09-13T18:07:08Z
dc.date.issued
2016-04
dc.identifier.citation
Clark, W. Edwin; Saito, Masahico; Vendramin, Claudio Leandro; Quandle coloring and cocycle invariants of composite knots and abelian extensions; World Scientific; Journal Of Knot Theory And Its Ramifications; 25; 5; 4-2016; 1650024
dc.identifier.issn
0218-2165
dc.identifier.uri
http://hdl.handle.net/11336/59552
dc.description.abstract
Quandle colorings and cocycle invariants are studied for composite knots, and applied to chirality and abelian extensions. The square and granny knots, for example, can be distinguished by quandle colorings, so that a trefoil and its mirror can be distinguished by quandle coloring of composite knots. We investigate this and related phenomena. Quandle cocycle invariants are studied in relation to quandle coloring of the connected sum, and formulas are given for computing the cocycle invariant from the number of colorings of composite knots. Relations to corresponding abelian extensions of quandles are studied, and extensions are examined for the table of small connected quandles, called Rig quandles. Computer calculations are presented, and summaries of outputs are discussed.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
World Scientific
dc.rights
info:eu-repo/semantics/openAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.subject
Abelian Extensions
dc.subject
Cocycle Invariants
dc.subject
Colorings
dc.subject
Composite Knots
dc.subject
Quandle
dc.subject.classification
Matemática Pura
dc.subject.classification
Matemáticas
dc.subject.classification
CIENCIAS NATURALES Y EXACTAS
dc.title
Quandle coloring and cocycle invariants of composite knots and abelian extensions
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2018-09-13T13:15:18Z
dc.journal.volume
25
dc.journal.number
5
dc.journal.pagination
1650024
dc.journal.pais
Singapur
dc.description.fil
Fil: Clark, W. Edwin. University of South Florida; Estados Unidos
dc.description.fil
Fil: Saito, Masahico. University of South Florida; Estados Unidos
dc.description.fil
Fil: Vendramin, Claudio Leandro. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
dc.journal.title
Journal Of Knot Theory And Its Ramifications
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/10.1142/S0218216516500243
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://www.worldscientific.com/doi/abs/10.1142/S0218216516500243
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4918820/
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1407.5803
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