Localization of the Riemann-Roch character (Q5957484)
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scientific article; zbMATH DE number 1717484
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Localization of the Riemann-Roch character |
scientific article; zbMATH DE number 1717484 |
Statements
Localization of the Riemann-Roch character (English)
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8 December 2002
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quantization of compact manifolds
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moment map
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transversally elliptic symbol
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The Guillemin-Sternberg conjecture [\textit{V. Guillemin} and \textit{S. Sternberg}, Invent. Math. 67, 515-538 (1982; Zbl 0503.58018)] about the commutativity of geometric quantization and symplectic reduction, was proved by \textit{E. Meinrenken} [Adv. Math. 134, 240-277 (1998; Zbl 0929.53045)] and \textit{Y. Tian} and \textit{W. Zhang} [Invent. Math. 132, 229-259 (1998; Zbl 0944.53047)].NEWLINENEWLINENEWLINEThe present paper gives a \(K\)-theoretic approach to this conjecture, which provides a new proof of results obtained by Meinrenken and Tian-Zhang. Also, this new approach leads to a generalization for compact Lie group actions on manifolds that are not symplectic.
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