The simplicial volume of contractible 3-manifolds

We show that the simplicial volume of a contractible 3-manifold not homeomorphic to R3 is infinite. As a consequence, the Euclidean space may be characterized as the unique contractible 3-manifold with vanishing minimal volume, or as the unique contractible 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 there exists a contractible n-manifold with vanishing simplicial volume not homeomorphic to Rn. We also compute the spectrum of the simplicial volume of irreducible open 3-manifolds.