Annular Dehn fillings

Abstract

We show that if a simple 3-manifold $M$ has two Dehn fillings at distance $Δ\geq 4$, each of which contains an essential annulus, then $M$ is one of three specific 2-component link exteriors in $S^3$. One of these has such a pair of annular fillings with $Δ= 5$, and the other two have pairs with $Δ= 4$.