L-invariants of locally symmetric spaces
نویسنده
چکیده
Let X = G/K be a Riemannian symmetric space of the noncompact type, Γ ⊂ G a discrete, torsion-free, cocompact subgroup, and let Y = Γ\X be the corresponding locally symmetric space. In this paper we explain how the Harish-Chandra Plancherel Theorem for L(G) and results on (g,K)-cohomology can be used in order to compute the L-Betti numbers, the Novikov-Shubin invariants, and the L-torsion of Y in a uniform way 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 m = rkCG − rkCK of G. In particular, we show the nonvanishing of the L-torsion of Y whenever m = 1.
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