ON DIFFEOMORPHISMS OVER T2 -KNOTS

For a spun T2-knot {S4, S{k)) or a twisted spun 7"2-knot {S4, S{k)) of a nontrivial knot k in S3, there are infinitely many isotopy classes of embeddings of a 2-torus into a 4-sphere which have this r2-knot as their image. This is shown by solving the following question: Which isotopy classes of diffeomorphisms of S{k) or {S4, S{k)) have orientation-preserving diffeomorphisms of S4 as their extension?