International Journal of Mathematics and Mathematical Sciences
Volume 17 (1994), Issue 3, Pages 457-462

Product involutions with 0 or 1-dimensional fixed point sets on orientable handlebodies

Roger B. Nelson

Department of Mathematical Sciences, Ball State University, Muncie 47306-0590, IN, USA

Received 20 August 1992; Revised 19 July 1993

Copyright © 1994 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.


Let h be an involution with a 0 or 1-dimensional fixed point set on an orientable handlebody M. We show that obvious necessary conditions for fibering M as A×I so that h=τ×r with τ an involution of A and r reflection about the midpoint of I also turn out to be sufficient. We also show that such a “product” involution is determined by its fixed point set.