Reducible Dehn surgery and annular Dehn surgery

Ruifeng Qiu

Vol. 192 (2000), No. 2, 357–368

DOI: 10.2140/pjm.2000.192.357

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.

Milestones

Received: 8 December 1996

Revised: 10 September 1998

Published: 1 February 2000