Kyungpook Mathematical Journal 2022; 62(2): 363-388
Published online June 30, 2022
Copyright © Kyungpook Mathematical Journal.
Finite, Fiber-preserving Group Actions on Elliptic 3-manifolds
Department of Mathematics, St. Martin’s University Lacey, WA 98503, United States
e-mail : email@example.com
Received: May 16, 2020; Accepted: December 8, 2021
In two previous papers the author presented a general construction of finite, fiber- and orientation-preserving group actions on orientable Seifert manifolds. In this paper we restrict our attention to elliptic 3-manifolds. For illustration of our methods a constructive proof is given that orientation-reversing and fiber-preserving diffeomorphisms of Seifert manifolds do not exist for nonzero Euler class, in particular elliptic 3-manifolds. Each type of elliptic 3-manifold is then considered and the possible group actions that fit the given construction. This is shown to be all but a few cases that have been considered elsewhere. Finally, a presentation for the quotient space under such an action is constructed and a specific example is generated.
Keywords: geometry, topology, 3-manifolds, finite group actions, Seifert fiberings, elliptic