The simplicial volume of closed manifolds covered by H^2 x H^2

Abstract

We compute the value of the simplicial volume for closed, oriented Riemannian manifolds covered by ${\mathbb{H}}^2\times {\mathbb{H}}^2$ explicitly, thus in particular for products of closed hyperbolic surfaces. This gives the first exact value of a nonvanishing simplicial volume for a manifold of nonconstant curvature.

19 pages; added consequences: Milnor-Wood type inequality, nonexistence of affine structure

References in corpus (2)

• The Proportionality Principle of Simplicial Volume
• Simplicial volume of Hilbert modular varieties

Cited by in corpus (19)

• Degree theorems and Lipschitz simplicial volume for non-positively curved manifolds of finite volume
• The simplicial volume of hyperbolic manifolds with geodesic boundary
• The simplicial volume of 3-manifolds with boundary
• The simplicial volume of mapping tori of 3-manifolds
• The norm of the Euler class
• On the simplicial volume and the Euler characteristic of (aspherical) manifolds
• Brouwer degree, domination of manifolds, and groups presentable by products
• Geometric structures, Gromov norm and Kodaira dimensions
• Families of 4-manifolds with nontrivial stable cohomotopy Seiberg-Witten invariants, and normalized Ricci flow
• The generalized Chern conjecture for manifolds that are locally a product of surfaces
• Lower Bound for the Simplicial Volume of Closed Manifolds Covered by ${\mathbb{H}}^2\times {\mathbb{H}}^2\times {\mathbb{H}}^2$
• Branched covering simply-connected 4-manifolds
• Geometric structures, the Gromov order, Kodaira dimensions and simplicial volume
• Efficient cycles of hyperbolic manifolds
• Surface bundles over surfaces: new inequalities between signature, simplicial volume and Euler characteristic
• The Gromov norm of the quaternionic Kähler class
• New bounds for the simplicial volume of complex hyperbolic surfaces
• Geometric structures in Topology, Geometry, Global Analysis and Dynamics
• Milnor-Wood inequalities for manifolds locally isometric to a product of hyperbolic planes