REDUCIBLE AND partial derivative-REDUCIBLE HANDLE ADDITIONS

摘要

Let M be a simple 3-manifold with F a component of partial derivative M of genus at least two. For a slope a on F, we denote by M(alpha) the manifold obtained by attaching a 2-handle to M along a regular neighborhood of alpha on F. Suppose that alpha and beta are two separating slopes oil F such that M(alpha) and M(beta) are reducible. Then the distance between alpha and beta is at most 2. As a corollary, if g(F) = 2, then there is at most one separating slope gamma on F such that M(gamma) is either reducible or partial derivative-reducible.