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Subjects
53-XX Differential geometry
53Dxx Symplectic geometry, contact geometry
53D50 Geometric quantization

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Formal deformations of symplectic manifolds with boundary.

Ryszard Nest, Boris Tsygan (1996)

Journal für die reine und angewandte Mathematik

Formal geometric quantization

Paul-Émile Paradan (2009)

Annales de l’institut Fourier

Let $K$ be a compact Lie group acting in a Hamiltonian way on a symplectic manifold $(M, Ω)$ which is pre-quantized by a Kostant-Souriau line bundle. We suppose here that the moment map $Φ$ is proper so that the reduced space $M_{μ} : = Φ^{- 1} (K \cdot μ) / K$ is compact for all $μ$ . Then, we can define the “formal geometric quantization” of $M$ as $𝒬_{K}^{- \infty} (M) : = \sum_{μ \in \hat{K}} 𝒬 (M_{μ}) V_{μ}^{K} .$ The aim of this article is to study the functorial properties of the assignment $(M, K) \to 𝒬_{K}^{- \infty} (M)$ .

Currently displaying 1 – 2 of 2

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