  We introduce the (general) homotopy groups of spheres as link invariants for
Brunnian-type links through the investigations on the intersection subgroup of
the normal closures of the meridians of strongly nonsplittable links. The
homotopy groups measure the difference between the intersection subgroup and
symmetric commutator subgroup of the normal closures of the meridians and give
the invariants of the links obtained in this way. Moreover the higher
homotopy-group invariants can produce some links that could not be detected by
the Milnor invariants. Furthermore all homotopy groups of spheres can be
obtained from the geometric Massey products on links.
