Contractible open 3-manifolds which non-trivially cover only non-compact 3-manifolds

Abstract

Suppose $M$ is a closed, connected, orientable, \irr\ \3m\ such that $G={\pi }_1(M)$ is infinite. One consequence of Thurston's geometrization conjecture is that the universal covering space $\tilde{M}$ of $M$ must be \homeo\ to $\RRR$. This has been verified directly under several different additional assumptions on $G$. (See, for example, \cite{2}, \cite{3}, \cite{6}, \cite{19}.)

Cited by in corpus (2)

• Contractible open 3-manifolds with free covering translation groups
• R^2-irreducible universal covering spaces of P^2-irreducible open 3-manifolds