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Suppose M is a connected, open, orientable, irreducible 3-manifold which isnot homeomorphic to R^3. Given a compact 3-manifold J in M which satisfiescertain conditions, Brin and Thickstun have associated to it an openneighborhood V$ called an end reduction of M at J. It has some usefulproperties which allow one to extend to M various results known to hold for themore restrictive class of eventually end irreducible open 3-manifolds. In thispaper we explore the relationship of V and M with regard to their fundamentalgroups and their covering spaces. In particular we give conditions under whichthe inclusion induced homomorphism on fundamental groups is an isomorphism. Wealso show that if M has universal covering space homeomorphic to R^3, then sodoes V. This work was motivated by a conjecture of Freedman (later disproved byFreedman and Gabai) on knots in M which are covered by a standard set of linesin R^3.

End reductions, fundamental groups, and covering spaces of irreducible open 3–manifolds