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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm111-2-2,
author = {Michelle Bucher-Karlsson},
title = {The proportionality constant for the simplicial volume of locally symmetric spaces},
journal = {Colloquium Mathematicae},
volume = {111},
year = {2008},
pages = {183-198},
zbl = {1187.53042},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm111-2-2}
}
Michelle Bucher-Karlsson. The proportionality constant for the simplicial volume of locally symmetric spaces. Colloquium Mathematicae, Tome 111 (2008) pp. 183-198. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm111-2-2/