\(L^ 2\)-index theorems on locally symmetric spaces (Q909322)
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scientific article; zbMATH DE number 4137069
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | \(L^ 2\)-index theorems on locally symmetric spaces |
scientific article; zbMATH DE number 4137069 |
Statements
\(L^ 2\)-index theorems on locally symmetric spaces (English)
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1989
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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.
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semisimple Lie group
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maximal compact subgroup
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Atiyah-Singer index theorem
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