Myers, Robert2025-01-152025-01-151998Myers, R. (1998). R²-irreducible universal covering spaces of P²-irreducible open 3-manifolds. Pacific Journal of Mathematics, 185(2), pp. 327-345. https://doi.org/10.2140/pjm.1998.185.3270030-8730https://hdl.handle.net/20.500.14446/345773First published in Pacific Journal of Mathematics in Vol. 185 (1998), No. 2, published by Mathematical Sciences PublishersAn irreducible open 3-manifold W is R²-irreducible if it contains no non-trivial planes, i.e. given any proper embedded plane in W some component of W −II must have closure an embedded halfspace R² ×(0, ∞). In this paper it is shown that if M is a connected, P²-irreducible, open 3-manifold such that π₁(M) is finitely generated and the universal covering space M of M is R²-irreducible, then either M̃ is homeomorphic to R³ or π₁(M) is a free product of infinite cyclic groups and fundamental groups of closed, connected surfaces other than S² or P². Given any finitely generated group G of this form, uncountably many P²-irreducible, open 3-manifolds M are constructed with π₁(M) ≅ G such that the universal covering space M is R²-irreducible and not homeomorphic to R³; the M are pairwise non-homeomorphic. Relations are established between these results and the conjecture that the universal covering space of any irreducible, orientable, closed 3-manifold with infinite fundamental group must be homeomorphic to R³.application/pdfThis material has been previously published. In the Oklahoma State University Library's institutional repository this version is made available through the open access principles and the terms of agreement/consent between the author(s) and the publisher. The permission policy on the use, reproduction or distribution of the material falls under fair use for educational, scholarship, and research purposes. Contact Digital Resources and Discovery Services at lib-dls@okstate.edu or 405-744-9161 for further information.10.2140/pjm.1998.185.327Articlemathematical sciencespure mathematicsgeneral mathematicsORCID: 0009-0008-5271-4140 (Myers, R)ScopusID: 7403700679 (Myers, R)