As a generalization of the linking number, we construct a set of invariant numbers for two-component handlebody-links. These numbers are elementary divisors associated with the natural homomorphism from the first homology group of a component to that of the complement of another component.
"Linking numbers for handlebody-links." Proc. Japan Acad. Ser. A Math. Sci. 89 (4) 60 - 62, April 2013. https://doi.org/10.3792/pjaa.89.60