The simplicial volume of contractible 3-manifolds

We show that the simplicial volume of a contractible 3 3 -manifold not homeomorphic to R 3 \mathbb {R}^3 is infinite. As a consequence, the Euclidean space may be characterized as the unique contractible 3 3 -manifold with vanishing minimal volume, or as the unique contractible 3 3 -manifold supporting a complete finite-volume Riemannian metric with Ricci curvature uniformly bounded from below. In contrast, we show that in every dimension n ≥ 4 n\geq 4 there exists a contractible n n -manifold with vanishing simplicial volume not homeomorphic to R n \mathbb {R}^n . We also compute the spectrum of the simplicial volume of irreducible open 3 3 -manifolds.