International Journal of Mathematics and Mathematical Sciences
Volume 13 (1990), Issue 1, Pages 39-44
A decomposition into homeomorphic handlebodies with naturally equivalent involutions
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  extended the well-known result that any closed -manifold contains a handlebody such that is homeomorphic to in the case where is a compact -manifold with nonvoid boundary. We show that if is a compact -manifold with involution having -dimensional fixed point set, then contains an -invariant handlebody such that the involutions induced on and are naturally equivalent.