Riemannian foliations and geometric quantization

Yi Lin; Yiannis Loizides; Reyer Sjamaar; Yanli Song

doi:10.1016/j.geomphys.2024.105133

Riemannian foliations and geometric quantization

Yi Lin
, Yiannis Loizides
, Reyer Sjamaar
, Yanli Song

Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

We introduce geometric quantization for constant rank presymplectic structures with Riemannian null foliation and compact leaf closure space. We prove a quantization-commutes-with-reduction theorem in this context. Examples related to symplectic toric quasi-folds, suspensions of isometric actions of discrete groups, and K-contact manifolds are discussed.

Original language	English
Article number	105133
Journal	Journal of Geometry and Physics
Volume	198
DOIs	https://doi.org/10.1016/j.geomphys.2024.105133
State	Published - Feb 7 2024

Scopus Subject Areas

Mathematical Physics
General Physics and Astronomy
Geometry and Topology

Keywords

Geometric quantization
Riemannian foliations
Symplectic geometry

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10.1016/j.geomphys.2024.105133

Cite this

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title = "Riemannian foliations and geometric quantization",

abstract = "We introduce geometric quantization for constant rank presymplectic structures with Riemannian null foliation and compact leaf closure space. We prove a quantization-commutes-with-reduction theorem in this context. Examples related to symplectic toric quasi-folds, suspensions of isometric actions of discrete groups, and K-contact manifolds are discussed.",

keywords = "Geometric quantization, Riemannian foliations, Symplectic geometry",

author = "Yi Lin and Yiannis Loizides and Reyer Sjamaar and Yanli Song",

note = "Publisher Copyright: {\textcopyright} 2024 Elsevier B.V.",

year = "2024",

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day = "7",

doi = "10.1016/j.geomphys.2024.105133",

language = "English",

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T1 - Riemannian foliations and geometric quantization

AU - Lin, Yi

AU - Loizides, Yiannis

AU - Sjamaar, Reyer

AU - Song, Yanli

PY - 2024/2/7

Y1 - 2024/2/7

N2 - We introduce geometric quantization for constant rank presymplectic structures with Riemannian null foliation and compact leaf closure space. We prove a quantization-commutes-with-reduction theorem in this context. Examples related to symplectic toric quasi-folds, suspensions of isometric actions of discrete groups, and K-contact manifolds are discussed.

AB - We introduce geometric quantization for constant rank presymplectic structures with Riemannian null foliation and compact leaf closure space. We prove a quantization-commutes-with-reduction theorem in this context. Examples related to symplectic toric quasi-folds, suspensions of isometric actions of discrete groups, and K-contact manifolds are discussed.

KW - Geometric quantization

KW - Riemannian foliations

KW - Symplectic geometry

UR - https://www.scopus.com/pages/publications/85187243964

U2 - 10.1016/j.geomphys.2024.105133

DO - 10.1016/j.geomphys.2024.105133

M3 - Article

AN - SCOPUS:85187243964

SN - 0393-0440

VL - 198

JO - Journal of Geometry and Physics

JF - Journal of Geometry and Physics

M1 - 105133

ER -

Riemannian foliations and geometric quantization

Abstract

Scopus Subject Areas

Keywords

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