Surgery descriptions of orientation-reversing periodic maps on closed orientable 3-manifolds

Abstract We study surgery descriptions of orientation-reversing periodic diffeomorphisms of compact orientable 3-manifolds in terms of standard symmetries of model manifolds. We develop a method for reducing the singular set by equivariant Dehn surgery, eliminating singular points with orientation-preserving local symmetries and connecting surface components. For periodic diffeomorphisms with reduced singular sets, we prove that such surgery descriptions exist in $$S^3$$ S 3 whenever the singular set contains no surface or contains a separating surface. The remaining cases are addressed through generalized surgery descriptions on other model manifolds. Furthermore, we show that the surgery descriptions can be chosen so that every surgery coefficient is an integer or a half-integer.