  New constructions in group homology allow us to manufacture high-dimensional
manifolds with controlled simplicial volume. We prove that for every dimension
bigger than 3 the set of simplicial volumes of orientable closed connected
manifolds is dense in $\mathbb{R}_{\geq 0}$. In dimension 4 we prove that every
non-negative rational number is the simplicial volume of some orientable closed
connected 4-manifold. Our group theoretic results relate stable commutator
length to the $l^1$-semi-norm of certain singular homology classes in degree 2.
The output of these results is translated into manifold constructions using
cross-products and Thom realisation.
