Szego Projections and New Invariants for CR and Contact Manifolds (Analytic Geometry of the Bergman Kernel and Related Topics)
Year: 2006
Type: article
Abstract: In this paper we present the construction in [Po4] of several new invariants for CR and contact manifolds by looking at the noncommutative residue traces of various geometric $\Psi_{H}\mathrm{D}\mathrm{O}$ projections.In the CR setting these operators arise from the $\overline{\partial}_{b}$ -complex and include the Szeg\"o projections acting on $(p,q)$ -forms.In the contact setting they stem from the generalized Szeg\"o projections at arbitrary integer levels of Epstein-Melrose and from the contact complex of Rumin.In particular, we recover and extend recent results of Hirachi and Boutet de Monvel and answer a question of Fefferman.Furthermore, we give simple algebro-geometric arguments proving that Hirachi's invariant vanishes on strictly pseudoconvex CR manifolds of dimension $4m+1$ .
Source: 数理解析研究所講究録
Author: Raphaël Ponge
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W263099274