Abstract
This paper gives a proof that the universal cover of a closed 3-manifold built from three π1-injective handlebodies is homeomorphic to ℝ3. This construction is an extension to handlebodies of the conditions for gluing of three solid tori to produce non-Haken Seifert fibered manifolds with infinite fundamental group. This class of manifolds has been shown to contain non-Haken non-Seifert fibered manifolds.
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