Simplical volume of closed locally symmetric spaces of non-compact type

By J.-F. Lafont, Benjamin Schmidt. 2005

96 citations recorded by the source corpus.

We show that closed, locally symmetric spaces of non-compact type have positive simplicial volume. This gives a positive answer to a question that was first raised by (Gromov in Inst Hautes Études Sci Publ Math 56:5, 1982).

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/7c19258b67f0f04bf18afbf1366154594e674e59

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Generalizations of the Kolmogorov–Barzdin embedding estimates (2011, unknown): “is a locally symmetric space with negative Ricci curvature, then it is possible to apply simplex straightening, and the volume of a k-dimensional straight simplex was bounded by Lafont and Schmidt in [LS]. To apply the proof above, one also needs a bound on the volumes of straight simplices of dimen”
Maximal Representations of Surface Groups: Symplectic Anosov Structures (2005, background): “nter. Is the comparison map (5.1) surjective in all degrees? MAXIMAL REPRESENTATIONS OF SURFACE GROUPS 23 This turns out to be true for forms representing speciﬁc classes (see [38], [24], [58], [10], [51]) and in particular for the K¨ahler form was ﬁrst shown by Dupont [24]. In fact, with the assume”
Degree theorems and Lipschitz simplicial volume for nonpositively curved manifolds of finite volume (2007, methodology): “arse) Lipschitz. Using the simplicial volume (and the work by Connell-Farb, Thurston, Savage, and Bucher-Karlsson), Lafont LIPSCHITZ SIMPLICIAL VOLUME OF NON-POSITIVELY CURVED MANIFOLDS 5 and Schmidt [18] prove degree theorems for closed locally symmetric spaces including the exceptional cases. The ”