International Journal of Mathematics and Mathematical Sciences
Volume 17 (1994), Issue 3, Pages 457-462
doi:10.1155/S0161171294000669
Product involutions with 0 or 1-dimensional fixed point sets on orientable handlebodies
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.
Abstract
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.