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

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.

Keywords

• orientable handlebody
• involution
• invariant disk
• fixed point set.