Quandle coloring and cocycle invariants of composite knots and abelian extensions

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...

Descripción completa

Guardado en:
Detalles Bibliográficos
Autor principal: Vendramin, Leandro
Publicado: 2016
Materias:
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02182165_v25_n5_p_Clark
http://hdl.handle.net/20.500.12110/paper_02182165_v25_n5_p_Clark
Aporte de:
Descripción
Sumario: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.