In this paper we consider the finite groups that act fiber- and orientation-preservingly on closed, compact, and orientable Seifert manifolds that fiber over an orientable base space. We establish a method of constructing such group actions and then show that if an action satisfies a condition on the obstruction class of the Seifert manifold, it can be derived from the given construction. The obstruction condition is refined and the general structure of the finite groups that act via the construction is provided.
If the inline PDF is not rendering correctly, you can download the PDF file here.
 F. Bonahon Geometric structures on 3-manifolds in: R.J. Daverman R.B. Sher (eds.) Handbook of Geometric Topology Elsevier Amsterdam 2002 pp. 93–164.
 R.D. Canary and D. McCullough Homotopy Equivalences of 3-Manifolds and Deformation Theory of Kleinian Groups Mem. Amer. Math. Soc. 172 (2004) no. 812 218 pp.
 A.L. Edmonds A topological proof of the equivariant Dehn lemma Trans. Amer. Math. Soc. 297 (1986) no. 2 605–615.
 J. Hempel 3-Manifolds AMS Chelsea Publishing Providence 2004.
 M. Jankins and W. D. Neumann Lectures on Seifert Manifolds Brandeis Lecture Notes 2 Brandeis University Waltham 1983.
 J. Kalliongis and A. Miller The symmetries of genus one handlebodies Canad. J. Math. 43 (1991) no. 2 371–404.
 J. Kalliongis and R. Ohashi Finite actions on the 2-sphere the projective plane and I-bundles over the projective plane Ars Math. Contemp. 15 (2018) no. 2 297–321.
 J.M. Lee Smooth manifolds in: J.M. Lee Introduction to Smooth Manifolds Graduate Texts in Mathematics 218 Springer-Verlag New York 2003 pp. 1–29.
 W.H. Meeks and P. Scott Finite group actions on 3-manifolds Invent. Math. 86 (1986) no. 2 287–346.
 W.D. Neumann and F. Raymond Seifert manifolds plumbing μ-invariant and orientation reversing maps in: K.C. Millett (ed.) Algebraic and geometric topology Lecture Notes in Math. 664 Springer Berlin 1978 pp. 163–196.
 P. Scott The geometries of 3-manifolds Bull. London Math. Soc. 15 (1983) no. 5 401–487.