SEIFERT SURFACES OF KNOTS IN S4

This paper uses some ideas from 3-dimensional topology to study knots in S4. We show that the Poincare conjecture implies the existence of a non-fibered knot whose complement fibers homotopically. In a different direction, we show that Gromov’s norm is an obstruction to a knot having a Seifert surface made out of Seifert fibered spaces, and hence to being ribbon. We also prove that any 3-manifold is invertibly homology cobordant to a hyperbolic 3-manifold, so that every knot in S4 has a hyperbolic Seifert surface. © 1990 by Pacific Journal of Mathematics.