Cyclic p-group actions on ℝℙ3

Abstract

In this paper, we classify the smooth orientation preserving cyclic [Formula: see text]-group actions on the real projective space [Formula: see text] up equivalence, where two actions are equivalent if their images are conjugate in the group of self-diffeomorphisms. We view [Formula: see text] as the lens space [Formula: see text]. We show that any such action on [Formula: see text] is conjugate to a standard action explicitly defined, and we identify the quotient spaces of these actions. In addition, we enumerate the equivalence classes.