L²-invariants of locally symmetric spaces

الأصل · EN

We explain how the Harish-Chandra Plancherel Theorem and results in relative Lie algebra cohomology can be used in order to compute in a uniform way the L²-Betti numbers, the Novikov-Shubin invariants, and the L²-torsion of compact locally symmetric spaces thus completing results previously obtained by Borel, Lott, Mathai, Hess and Schick. It turns out that the behaviour of these invariants is essentially determined by the fundamental rank of the group of isometries of the corresponding globally symmetric space. In particular, we show the nonvanishing of the L²-torsion whenever the fundamental rank is equal to 1.