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Mat. Zametki, 2019, Volume 105, Issue 6, Pages 857–878 (Mi mz12068)  

This article is cited in 1 scientific paper (total in 1 paper)

Kostant Prequantization of Symplectic Manifolds with Contact Singularities

D. B. Zot'evab

a Volzhsk Branch of Moscow Power Engineering Institute
b Volgograd State Technical University

Abstract: 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.

Keywords: quantization, Kostant–Souriau quantization, Bohr–Sommerfeld conditions, contact singularity, $\Theta$-handle.

DOI: https://doi.org/10.4213/mzm12068

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English version:
Mathematical Notes, 2019, 105:6, 846–863

Bibliographic databases:

UDC: 514.7
Received: 22.05.2018
Revised: 08.11.2018

Citation: D. B. Zot'ev, “Kostant Prequantization of Symplectic Manifolds with Contact Singularities”, Mat. Zametki, 105:6 (2019), 857–878; Math. Notes, 105:6 (2019), 846–863

Citation in format AMSBIB
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\paper Kostant Prequantization of Symplectic Manifolds with Contact Singularities
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\issue 6
\pages 857--878
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  • https://doi.org/10.4213/mzm12068
  • http://mi.mathnet.ru/eng/mz/v105/i6/p857

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. Bravetti, M. de Leon, J. C. Marrero, E. Padron, “Invariant measures for contact Hamiltonian systems: symplectic sandwiches with contact bread”, J. Phys. A-Math. Theor., 53:45 (2020), 455205  crossref  mathscinet  isi
  • Математические заметки Mathematical Notes
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