4 papers
A condition of admissibility for generalized Alexander quandles
Katsunori Arai, Keisuke Himeno, Ryoya Kai +1
A typical example of a quandle is the conjugation quandle. A quandle is said to be admissible if it is isomorphic to a conjugation quandle. We study the admissibility problem for q…
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…
Infinitely many pairs of spatial surfaces
Katsunori Arai
A multiple group rack (MGR) is an algebraic system which is used to construct invariants of spatial surfaces, which are compact surfaces embedded in the -sphere . Seifert…
A construction of multiple group racks
Katsunori Arai
A multiple group rack is a rack which is a disjoint union of groups equipped with a binary operation satisfying some conditions. It is used to define invariants of spatial surfaces…