Mathematical Proceedings of the Cambridge Philosophical Society

Research Article

Knot surgery and primeness

Francisco González Acuñaa1 and Hamish Shorta2

a1 Instituto de Matemáticas, Universidad National Autonoma de México

a2 Department of Pure Mathematics, University of Liverpool

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

S0305004100063969_eqnU1

one of M1, M2 is S3. (For standard definitions of low-dimensional topology see [2] or [16].)

(Received August 08 1984)

(Revised February 11 1985)