Abstract
Suppose Δ⊂ S 3 is a ribbon disk and let D ( Δ) denote the cononical properly embedded 2-disk obtained by pushing the interior of Δ into B 4. A well-known conjecture states that the disk pair ( B 4, D( Δ)) is trivial provided the sphere pair ∂( B 4, D( Δ)) is trivial. We show here that the conjecture is true for those D( Δ) with the property that there is an embedded 2-disk, D 2⊂ S 3, whose boundary is ∂ D( Δ) and which intersects Δ in ‘transverse double points’.
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