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Paradan, Paul-Emile

Localization of the Riemann-Roch character. (English) Zbl 1001.53062

J. Funct. Anal. 187, No. 2, 442-509 (2001).
The Guillemin-Sternberg conjecture [V. Guillemin and S. Sternberg, Invent. Math. 67, 515-538 (1982; Zbl 0503.58018)] about the commutativity of geometric quantization and symplectic reduction, was proved by E. Meinrenken [Adv. Math. 134, 240-277 (1998; Zbl 0929.53045)] and Y. Tian and W. Zhang [Invent. Math. 132, 229-259 (1998; Zbl 0944.53047)].
The 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.
Reviewer: Mircea Crâşmăreanu (Iaşi)

Cited in 5 Reviews
Cited in 39 Documents

MSC:

53D50 Geometric quantization
55R50 Stable classes of vector space bundles in algebraic topology and relations to \(K\)-theory

Keywords:

quantization of compact manifolds; moment map; transversally elliptic symbol

Citations:

Zbl 0503.58018; Zbl 0929.53045; Zbl 0944.53047
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Full Text: DOI arXiv

References:

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