On the homeomorphisms of a non-orientable surface

Abstract

The purpose of this note is to answer a question asked in an earlier paper ((2), page 315). Let X be a closed, connected, non-orientable 2-manifold and f: X → X a homeomorphism. It was shown in (2) that f is isotopic to a product of homeomorphisms of two basic types, the c-homeomorphism, which will now be called a twist, and the Y-homeomorphism (see (2) for definitions). It was also proved that f cannot, in general, be expressed as a product of twists alone. The following result is proved here: