分野別セミナー

In his famous survey article “A Quick Trip through Knot Theory”,
Ralph Fox used the motion-picture method to construct a
2-knot with group having commutator subgroup the dyadic rationals.
This knot (his Example 10) is in fact a ribbon 2-knot,
and so is determined by its exterior.
We shall show that it is determined up to topological isotopy
and reflection by its group.
This is an application of ideas used in studying the homotopy types of
``strongly minimal" 4-manifolds,
with fundamental groups of geometric dimension 2.
(Once the homotopy type of the knot manifold is known,
the result follows easily from known surgery arguments.)