Geodesic
Kostant Prequantization of Symplectic Manifolds with Contact Singularities
Matematičeskie zametki, Tome 105 (2019) no. 6, pp. 857-878

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The relationship between the Bohr–Sommerfeld quantization condition and the integrality of the symplectic structure in Planck constant units is considered. Constructions of spherical and toric $\Theta$-handles are proposed which allow one to obtain symplectic manifolds with contact singularities, preserve Kostant–Souriau prequantization, and expect interesting topological applications. In particular, the toric $\Theta$-handle glues Liouville foliations, while the spherical handle generates (pre)quantized connected sums of symplectic manifolds. In this way, nonorientable manifolds may arise.
Mots-clés : quantization, Kostant–Souriau quantization
Keywords: Bohr–Sommerfeld conditions, contact singularity, $\Theta$-handle. 
@article{MZM_2019_105_6_a4,
     author = {D. B. Zot'ev},
     title = {Kostant {Prequantization} of {Symplectic} {Manifolds} with {Contact} {Singularities}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {857--878},
     publisher = {mathdoc},
     volume = {105},
     number = {6},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2019_105_6_a4/}
}
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D. B. Zot'ev. Kostant Prequantization of Symplectic Manifolds with Contact Singularities. Matematičeskie zametki, Tome 105 (2019) no. 6, pp. 857-878. http://geodesic.mathdoc.fr/item/MZM_2019_105_6_a4/