CONICET | Buscador de Institutos y Recursos Humanos

Quandle colorings and cocycle invariants are studied for composite knots, andapplied to chirality and abelian extensions. The square and granny knots, forexample, can be distinguished by quandle colorings, so that a trefoil and itsmirror can be distinguished by quandle invariants of composite knots. Weinvestigate this and related phenomena. Quandle cocycle invariants are studiedin relation to the connected sum, and formulas are given for computing thecocycle invariant from the number of colorings of composite knots. Relations tocorresponding abelian extensions of quandles are studied, and extensions areexamined for the table of small connected quandles, called Rig quandles.Computer calculations are presented, and summaries of outputs are discussed.