Quantization of Presymplectic Manifolds and Circle Actions

1997/05/17 by Ana Canas da Silva, Yael Karshon, da Silva, Ana Canas +3
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.dg-ga/9705008

openalex publication_date 1997/05/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove several versions of "quantization commutes with reduction" for circle actions on manifolds that are not symplectic. Instead, these manifolds possess a weaker structure, such as a spin^c structure. Our theorems work whenever the quantization data and the reduction data are compatible; this condition always holds if we start from a presymplectic (in particular, symplectic) manifold.

Citations

• Bott towers, complete integrability, and the extended character of representations
• Geometric quantization and multiplicities of group representations

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