4 papers · 1 filter
Detecting non-admissibility of quandles via colorings
Katsunori Arai, Ryoya Kai
A quandle is an algebraic system whose axioms are motivated by Reidemeister moves in knot theory. A typical example is a conjugation quandle arising from a group. A quandle is said…
Metrics for quandles
Kohei Iwamoto, Ryoya Kai, Yuya Kodama
A quandle is an algebraic system originating in knot theory, which can be regarded as a generalization of the conjugation of groups. This structure naturally defines two subgroups…
On the Euler characteristics for quandles
Ryoya Kai, Hiroshi Tamaru
A quandle is an algebraic system whose axioms generalize the algebraic structure of the point symmetries of symmetric spaces. In this paper, we give a definition of Euler character…
On the quandles of isometries of the hyperbolic 3-space
Ryoya Kai
A quandle is an algebraic structure whose axioms are related to the Reidemeister moves used in knot theory. In this paper, we investigate the conjugate quandle of the orientation-p…