Localization of the Riemann-Roch character

Paul-Emile Paradan (1)

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier

We present a K-theoretic 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.

Mots clés: moment map; reduction; geometric quantization; induction; transversally elliptic symbol

Domaines: Géométrie symplectique [math.SG]

Paul-Emile Paradan. Localization of the Riemann-Roch character. Journal of Functional Analysis, 2001, 187 (2), pp.442-509. ⟨10.1006/jfan.2001.3825⟩. ⟨hal-00773250⟩