2006/01/21 by Sarah Hansoul, Hansoul, S.
Mathematics · Physics and Astronomy · #46L65 #53B05 #58A05 #58J70 #Advanced Differential Geometry Research #Advanced Topics in Algebra #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.math/0601518
openalex publication_date 2006/01/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the existence of natural and projectively equivariant quantizations for differential operators acting between order 1 vector bundles over a smooth manifold M. To that aim, we make use of the Thomas-Whitehead approach of projective structures and construct a Casimir operator depending on a projective Cartan connection. We attach a scalar parameter to every space of differential operators, and prove the existence of a quantization except when this parameter belongs to a discrete set of resonant values.