Abstract. We compute the value of the simplicial volume for closed, oriented Riemannian manifolds covered by H 2 × H 2 explicitly, thus in particular for products of closed hyperbolic surfaces. This gives the first exact value of a nonvanishing simplicial volume for a manifold not admitting a hyperbolic structure.

We give the first complete proof of the strict positivity of the simplicial volume of compact locally symmetric spaces covered by SL 3 R/SO(3) and show why the proof in [Savage RP, Trans Amer Math Soc 274(1):239-263, 1982] is incorrect.

Abstract. We follow ideas going back to Gromov's seminal article [Publ. Math. IHES 56 (1982)] to show that the proportionality constant relating the simplicial volume and the volume of a closed, oriented, locally symmetric space M = Γ \G/K of noncompact type is equal to the Gromov norm of the volume form in the continuous cohomology of G. The proportionality constant thus becomes easier to compute. Furthermore, this method also gives a simple proof of the proportionality principle for arbitrary manifolds.

No abstract

We give new lower bounds for the minimal number of simplices needed in a triangulation of the product of two convex polygons, improving the lower bounds in Bowen et al. (Topology 44:321-339, 2005).