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\(L^ 2\)-index theorems on locally symmetric spaces. (English) Zbl 0694.58039

Let G be a real semisimple Lie group, K a maximal compact subgroup, and \(\Gamma\) a neat arithmetic subgroup. If the \({\mathbb{Q}}\)-rank of G is greater than zero, then \(\Gamma\setminus G/K\) is a noncompact, finite volume, locally symmetric space. The main aim of this paper is to extend the Atiyah-Singer index theorem to an \(L^ 2\)-index theorem in this situation.
Reviewer: V.Deundyak

MSC:

58J20 Index theory and related fixed-point theorems on manifolds
53C35 Differential geometry of symmetric spaces
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References:

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