Localization of the Riemann-Roch character

Details Localization of the Riemann-Roch character Localization of the Riemann-Roch character

1999-11-04

arxiv.org/abs/math/9911024v2

Mathematics

Differential Geometry

revised version, 55 pages

Scientific paper

We present a K-theoritic approach to the Guillemin-Sternberg conjecture, about the commutativity of geometric quantization and symplectic reduction, which was proved by Meinrenken and Tian-Zhang. Besides providing a new proof of this conjecture for the full non-abelian group action case, our methods lead to a generalisation for compact Lie group actions on manifolds that are not symplectic. Instead, these manifolds carry an invariant almost complex structure and an abstract moment map.

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