R^{2}-IRREDUCIBLE UNIVERSAL COVERING SPACES OF P^{2}-IRREDUCIBLE OPEN 3-MANIFOLDS

ROBERT MYERS

Abstract. An irreducible open 3-manifold W is R^{2}-irreducible if every proper plane in W splits off a halfspace. In this paper it is shown that if such a W is the universal cover of a connected, P^{2}-irreducible open 3-manifold M with finitely generated fundamental group, then either W is homeomorphic to R^{3} or the group is a free product of infinite cyclic groups and infinite closed surface groups. Given any such finitely generated group uncountably many M are constructed with that fundamental group such that their universal covers are R^{2}-irreducible, are not homeomorphic to R^{3}, and are pairwise non-homeomorphic. These results are related to the conjecture that closed, orientable, irreducible, aspherical 3-manifolds are covered by R^{3}.