∂-Reducible handle additions

摘要

Let M be a simple 3-manifold, and F be a component of partial derivative M of genus at least 2. Let alpha and beta be separating slopes on F. Let M(alpha) (resp. M(beta)) be the manifold obtained by adding a 2-handle along a (resp. beta). If M(alpha) and M(beta) are a-reducible, then the minimal geometric intersection number of alpha and beta is at most 8. (C) 2019 Elsevier B.V. All rights reserved.