Abstract

Let M be a compact, orientable, irreducible, ∂-irreducible, anannular 3-manifold with one component T of ∂M a torus. Suppose that r₁ and r₂ are two slopes on T. In this paper, we shall show that if M(r₁) is reducible while M(r₂) contains an essential annulus, then △(r₁,r₂) ≤ 2.

Authors