The proportionality constant for the simplicial volume of locally symmetric spaces
Tom 111 / 2008
Colloquium Mathematicum 111 (2008), 183-198
MSC: 22E41, 53C35.
DOI: 10.4064/cm111-2-2
Streszczenie
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 $M={\mit\Gamma }\backslash G /K$ 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.
