title: Quandle coloring and cocycle invariants of composite knots and abelian extensions.
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.
authors.affiliation: Department of Mathematics and Statistics, University of South Florida, Tampa, Florida, USA.
authors.forename: W Edwin
authors.initials: WE
authors.lastname: Clark
authors.affiliation: Department of Mathematics and Statistics, University of South Florida, Tampa, Florida, USA.
authors.forename: Masahico
authors.initials: M
authors.lastname: Saito
authors.affiliation: Departamento de Mathemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires Buenos Aires, Argentina.
authors.forename: Leandro
authors.initials: L
authors.lastname: Vendramin
keywords: Quandle; abelian extensions; cocycle invariants; colorings; composite knots