A $G$-family of quandles and handlebody-knots
  We introduce the notion of a $G$-family of quandles which is an algebraic system whose axioms are motivated by handlebody-knot theory, and use it to construct invariants for handlebody-knots. Our invariant can detect the chiralities of some handlebody-knots including unknown ones. 
Atsushi Ishii, Masahide Iwakiri, Yeonhee Jang, Kanako Oshiro
math.GT