Geometric quantization for proper actions

DOI10.1016/j.aim.2010.03.023zbMath1211.53101arXiv0806.3138OpenAlexW2114621361MaRDI QIDQ2637909

Weiping Zhang, Varghese Mathai

Publication date: 13 September 2010

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0806.3138

zbMATH Keywords

equivariant \(K\)-theorygeometric quantizationlocally compact groupsGuillemin-Sternberg conjectureHochs-Landsman conjectureindex theorem for generalized orbifolds

Mathematics Subject Classification ID

Index theory and related fixed-point theorems on manifolds (58J20) Spin and Spin({}^c) geometry (53C27) Momentum maps; symplectic reduction (53D20) Geometric quantization (53D50)

Related Items (23)

Hopf cyclic cohomology and Hodge theory for proper actions on complex manifolds ⋮ Formal geometric quantisation for proper actions ⋮ Quantization commutes with reduction, a survey ⋮ An equivariant index for proper actions. I ⋮ An equivariant index for proper actions. III: The invariant and discrete series indices ⋮ Hodge theory for non-compact \(G\)-manifolds with boundary ⋮ Index of equivariant Callias-type operators and invariant metrics of positive scalar curvature ⋮ Hopf cyclic cohomology and Hodge theory for proper actions ⋮ Positive scalar curvature and Poincaré duality for proper actions ⋮ An equivariant orbifold index for proper actions ⋮ The index theory on non-compact manifolds with proper group action ⋮ A geometric realisation of tempered representations restricted to maximal compact subgroups ⋮ Positive scalar curvature and an equivariant Callias-type index theorem for proper actions ⋮ A \(K\)-homological approach to the quantization commutes with reduction problem ⋮ Spectral theory of von Neumann algebra valued differential operators over non-compact manifolds ⋮ Quantization commutes with singular reduction: Cotangent bundles of compact Lie groups ⋮ Geometric quantization and families of inner products ⋮ Hopf cyclic cohomology for noncompact \(G\)-manifolds with boundary ⋮ Witten Non Abelian Localization for Equivariant K-Theory, and the [𝑄,𝑅=0 Theorem] ⋮ Quantisation of presymplectic manifolds, $K$-theory and group representations ⋮ Coarse geometry and Callias quantisation ⋮ A vanishing theorem for the Mathai-Zhang index ⋮ Elliptic boundary value problem on non-compact G-manifolds

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• Complex immersions and Quillen metrics
• Symplectic surgery and the Spin\(^c\)-Dirac operator
• Symplectic reduction and a weighted multiplicity formula for twisted \(\text{Spin}^c\)-Dirac operators
• Signature quantization
• Poisson geometry of discrete series orbits, and momentum convexity for noncompact group actions

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