Proportionality principle for the simplicial volume of families of \(\mathbb Q\)-rank 1 locally symmetric spaces (Q2636968)

The simplicial volume of a closed hyperbolic manifold was introduced by Gromov in the early 1980s. Gromov-Thurston established an important proportionality principle of the volume of a Riemannian manifold \((M,g)\) and the simplicial volume of \(M\), depending only on the universal cover of \((M,g)\). The authors establish a similar proportionality principle between the Riemannian volume and the simplicial volume of \(\mathbb Q\)-rank 1 locally symmetric spaces, covered by products of hyperbolic spaces. As an application, they construct manifolds whose cusp groups are not necessarily amenable.