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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. © 2016 World Scientific Publishing Company.

Registro:

Documento: Artículo
Título:Quandle coloring and cocycle invariants of composite knots and abelian extensions
Autor:Clark, W.E.; Saito, M.; Vendramin, L.
Filiación:Department of Mathematics and Statistics, University of South Florida, Tampa, FL, United States
Departamento de Mathemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires, Argentina
Palabras clave:abelian extensions; cocycle invariants; colorings; composite knots; Quandle
Año:2016
Volumen:25
Número:5
DOI: http://dx.doi.org/10.1142/S0218216516500243
Título revista:Journal of Knot Theory and its Ramifications
Título revista abreviado:J. Knot Theory Ramifications
ISSN:02182165
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02182165_v25_n5_p_Clark

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Citas:

---------- APA ----------
Clark, W.E., Saito, M. & Vendramin, L. (2016) . Quandle coloring and cocycle invariants of composite knots and abelian extensions. Journal of Knot Theory and its Ramifications, 25(5).
http://dx.doi.org/10.1142/S0218216516500243
---------- CHICAGO ----------
Clark, W.E., Saito, M., Vendramin, L. "Quandle coloring and cocycle invariants of composite knots and abelian extensions" . Journal of Knot Theory and its Ramifications 25, no. 5 (2016).
http://dx.doi.org/10.1142/S0218216516500243
---------- MLA ----------
Clark, W.E., Saito, M., Vendramin, L. "Quandle coloring and cocycle invariants of composite knots and abelian extensions" . Journal of Knot Theory and its Ramifications, vol. 25, no. 5, 2016.
http://dx.doi.org/10.1142/S0218216516500243
---------- VANCOUVER ----------
Clark, W.E., Saito, M., Vendramin, L. Quandle coloring and cocycle invariants of composite knots and abelian extensions. J. Knot Theory Ramifications. 2016;25(5).
http://dx.doi.org/10.1142/S0218216516500243