A decomposition into homeomorphic handlebodies with naturally equivalent involutions

Abstract

Downing [6] extended the well-known result that any closed 3-manifold X contains a handlebody H such that c1(X−H) is homeomorphic to H in the case where X is a compact 3-manifold with nonvoid boundary. We show that if X is a compact 3-manifold with involution h having 2-dimensional fixed point set, then X contains an h-invariant handlebody H such that the involutions induced on H and c1(X−H) are naturally equivalent.