The analytic index for proper, Lie groupoid actions (Q2785086)
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scientific article; zbMATH DE number 1733302
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The analytic index for proper, Lie groupoid actions |
scientific article; zbMATH DE number 1733302 |
Statements
7 October 2002
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operator K-theory
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index theorem
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Lie groupoid
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math.OA
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math.KT
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The analytic index for proper, Lie groupoid actions (English)
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\textit{A. Connes} observed that a number of index theorems are all special cases of the same index theorem for \(G\)-invariant elliptic operators \(D\) on a proper \(G\)-manifold X, \(G\) being a Lie groupoid. The present paper establishes this under certain conditions. The approach to the analytic index \(i^a(D) (\in K_0(C^*(G)))\) of \(D\) is based on an adaptation of the classical equivariant Atiyah-Singer index theorem for families.NEWLINENEWLINEFor the entire collection see [Zbl 0972.00029].
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