The proportionality constant for the simplicial volume of locally symmetric spaces

Volume 111 / 2008

Michelle Bucher-Karlsson Colloquium Mathematicum 111 (2008), 183-198 MSC: 22E41, 53C35. DOI: 10.4064/cm111-2-2

Abstract

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.

Authors

  • Michelle Bucher-KarlssonMath. Dept. KTH
    SE-100 44 Stockholm, Sweden
    e-mail

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