The universal cover of 3-manifolds built from injective handlebodies is $\mathbb R^3$

James Coffey

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The universal cover of 3-manifolds built from injective handlebodies is $\mathbb R^3$

James Coffey

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Abstract

This paper gives a proof that the universal cover of a closed 3-manifold built from three $π_1$-injective handlebodies is homeomorphic to $\mathbb R^3$. 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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James Coffey. 2007-01-31. The universal cover of 3-manifolds built from injective handlebodies is $\mathbb R^3$. https://arxiv.org/abs/math/0601721

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