International Journal of Mathematics and Mathematical Sciences
Volume 13 (1990), Issue 1, Pages 39-44

A decomposition into homeomorphic handlebodies with naturally equivalent involutions

Roger B. Nelson

Department of Mathematical Sciences, Ball State University, Muncie 47306, IN, USA

Copyright © 1990 Roger B. Nelson. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Downing [6] extended the well-known result that any closed 3-manifold X contains a handlebody H such that c1(XH) 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(XH) are naturally equivalent.