Knot surgery and primeness

Abstract

The aim of this paper is to prove some new results towards answering the question: When does Dehn surgery on a knot give a non-prime manifold ? This question has been raised on several occasions (see for instance [5] or [4]; concerning the latter see below). Recall that a 3-manifold is prime if, in any connected sum decomposition one of M 1 , M 2 is S 3 . (For standard definitions of low-dimensional topology see [2] or [16].)