13:00--14:30 E404



On higher order linking numbers for handlebody-links

J. Milnor introduced an equivalence relation on links, called link-homotopy, which is generated by ambient isotopy and self-crossing changes. He also gave a stronger invariant under link-homotopy as a generalization of the linking number, called higher order linking numbers.In this talk, by using higher order linking numbers, we construct a link-homotopy invariant for handlebody-links, which is a disjoint union of handlebodies embedded in $S^3$. We also give a bijection between the set of link-homotopy classes of $n$-component handlebody-links with some assumption and a quotient of the action of the general linear group on a tensor product of modules. This is joint work with Atsuhiko Mizusawa.