Artículos de revistas
Quandle coloring and cocycle invariants of composite knots and abelian extensions
Fecha
2016-04Registro en:
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
Autor
Clark, W. Edwin
Saito, Masahico
Vendramin, Claudio Leandro
Resumen
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.