Finite, fiber- and orientation-preserving actions on orientable Seifert manifolds with non-orientable base space

Abstract

This paper extends the results from the author's previous paper to consider finite, fiber- and orientation- preserving group actions on closed, orientable Seifert manifolds $M$ that fiber over a non-orientable base space. An orientable base space double cover $\tilde{M}$ of $M$ is constructed and then an isomorphism between the fiber- and orientation-preserving diffeomorphisms of ${M}$ and the fiber- and orientation-preserving actions on $\tilde{M}$ that preserve the orientation on the fibers and commute with the covering translation is shown. This result and previous results lead to a construction of all actions that satisfy a condition on the obstruction term and the structure of the finite groups that can act on $M$.