New bounds for the simplicial volume of complex hyperbolic surfaces

Abstract

We give estimates of the Gromov norm of the top dimensional class in $H_c^4(\mathrm{Isom}({\mathbb{H}}_{\mathbb{C}}^2);\mathbb{R})$. As a consequence, we obtain an explicit upper bound for the simplicial volume of closed oriented manifolds that are locally isometric to ${\mathbb{H}}_{\mathbb{C}}^2$.

14 pages