Quandle coloring and cocycle invariants of composite knots and abelian extensions

Autores
Clark, W. Edwin; Saito, Masahico; Vendramin, Claudio Leandro
Año de publicación
2016
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
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.
Fil: Clark, W. Edwin. University of South Florida; Estados Unidos
Fil: Saito, Masahico. University of South Florida; Estados Unidos
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
Materia
ABELIAN EXTENSIONS
COCYCLE INVARIANTS
COLORINGS
COMPOSITE KNOTS
QUANDLE
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/59552
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/59552
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Quandle coloring and cocycle invariants of composite knots and abelian extensionsClark, W. EdwinSaito, MasahicoVendramin, Claudio LeandroABELIAN EXTENSIONSCOCYCLE INVARIANTSCOLORINGSCOMPOSITE KNOTSQUANDLEhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Quandle 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.Fil: Clark, W. Edwin. University of South Florida; Estados UnidosFil: Saito, Masahico. University of South Florida; Estados UnidosFil: Vendramin, Claudio Leandro. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaWorld Scientific2016-04info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/59552Clark, 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; 16500240218-2165CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1142/S0218216516500243info:eu-repo/semantics/altIdentifier/url/https://www.worldscientific.com/doi/abs/10.1142/S0218216516500243info:eu-repo/semantics/altIdentifier/url/https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4918820/info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1407.5803info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:37:16Zoai:ri.conicet.gov.ar:11336/59552instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 10:37:16.517CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Quandle coloring and cocycle invariants of composite knots and abelian extensions
title Quandle coloring and cocycle invariants of composite knots and abelian extensions
spellingShingle Quandle coloring and cocycle invariants of composite knots and abelian extensions
Clark, W. Edwin
ABELIAN EXTENSIONS
COCYCLE INVARIANTS
COLORINGS
COMPOSITE KNOTS
QUANDLE
title_short Quandle coloring and cocycle invariants of composite knots and abelian extensions
title_full Quandle coloring and cocycle invariants of composite knots and abelian extensions
title_fullStr Quandle coloring and cocycle invariants of composite knots and abelian extensions
title_full_unstemmed Quandle coloring and cocycle invariants of composite knots and abelian extensions
title_sort Quandle coloring and cocycle invariants of composite knots and abelian extensions
dc.creator.none.fl_str_mv Clark, W. Edwin
Saito, Masahico
Vendramin, Claudio Leandro
author Clark, W. Edwin
author_facet Clark, W. Edwin
Saito, Masahico
Vendramin, Claudio Leandro
author_role author
author2 Saito, Masahico
Vendramin, Claudio Leandro
author2_role author
author
dc.subject.none.fl_str_mv ABELIAN EXTENSIONS
COCYCLE INVARIANTS
COLORINGS
COMPOSITE KNOTS
QUANDLE
topic ABELIAN EXTENSIONS
COCYCLE INVARIANTS
COLORINGS
COMPOSITE KNOTS
QUANDLE
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv 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.
Fil: Clark, W. Edwin. University of South Florida; Estados Unidos
Fil: Saito, Masahico. University of South Florida; Estados Unidos
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
description 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.
publishDate 2016
dc.date.none.fl_str_mv 2016-04
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/59552
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
0218-2165
CONICET Digital
CONICET
url http://hdl.handle.net/11336/59552
identifier_str_mv 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
0218-2165
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1142/S0218216516500243
info:eu-repo/semantics/altIdentifier/url/https://www.worldscientific.com/doi/abs/10.1142/S0218216516500243
info:eu-repo/semantics/altIdentifier/url/https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4918820/
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1407.5803
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv World Scientific
publisher.none.fl_str_mv World Scientific
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.070432

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