A decomposition into homeomorphic handlebodies with naturally equivalent involutions
Roger B. Nelson · International Journal of Mathematics and Mathematical Sciences · 1990
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.