The proportionality constant for the simplicial volume of locally symmetric spaces

Michelle Bucher-Karlsson¹

¹ Math. Dept. KTH SE-100 44 Stockholm, Sweden

Colloquium Mathematicum, Tome 111 (2008) no. 2, pp. 183-198.

Résumé

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.

Détail

DOI : 10.4064/cm111-2-2

Keywords: follow ideas going back gromovs seminal article publ math ihes proportionality constant relating simplicial volume volume closed oriented locally symmetric space mit gamma backslash noncompact type equal gromov norm volume form continuous cohomology proportionality constant becomes easier compute furthermore method gives simple proof proportionality principle arbitrary manifolds