On the index theorem for symplectic orbifolds

Boris Fedosov[1]; Bert-Wolfang Schulze; Nikolai Tarkhanov

  • [1] Universität Potsdam, Institut für Mathematik, Postfach 60 15 53, 14415 Potsdam (Allemagne)

Annales de l’institut Fourier (2004)

  • Volume: 54, Issue: 5, page 1601-1639
  • ISSN: 0373-0956

Abstract

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We give an explicit construction of the trace on the algebra of quantum observables on a symplectiv orbifold and propose an index formula.

How to cite

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Fedosov, Boris, Schulze, Bert-Wolfang, and Tarkhanov, Nikolai. "On the index theorem for symplectic orbifolds." Annales de l’institut Fourier 54.5 (2004): 1601-1639. <http://eudml.org/doc/116154>.

@article{Fedosov2004,
abstract = {We give an explicit construction of the trace on the algebra of quantum observables on a symplectiv orbifold and propose an index formula.},
affiliation = {Universität Potsdam, Institut für Mathematik, Postfach 60 15 53, 14415 Potsdam (Allemagne)},
author = {Fedosov, Boris, Schulze, Bert-Wolfang, Tarkhanov, Nikolai},
journal = {Annales de l’institut Fourier},
keywords = {star-product; symmetry group; G-trace; G-index; orbifold; index theorem; deformation quantization; traces},
language = {eng},
number = {5},
pages = {1601-1639},
publisher = {Association des Annales de l'Institut Fourier},
title = {On the index theorem for symplectic orbifolds},
url = {http://eudml.org/doc/116154},
volume = {54},
year = {2004},
}

TY - JOUR
AU - Fedosov, Boris
AU - Schulze, Bert-Wolfang
AU - Tarkhanov, Nikolai
TI - On the index theorem for symplectic orbifolds
JO - Annales de l’institut Fourier
PY - 2004
PB - Association des Annales de l'Institut Fourier
VL - 54
IS - 5
SP - 1601
EP - 1639
AB - We give an explicit construction of the trace on the algebra of quantum observables on a symplectiv orbifold and propose an index formula.
LA - eng
KW - star-product; symmetry group; G-trace; G-index; orbifold; index theorem; deformation quantization; traces
UR - http://eudml.org/doc/116154
ER -

References

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  1. M. F. Atiyah, Elliptic operators and compact groups, 401 (1974), Springer-Verlag, Berlin Zbl0297.58009MR482866
  2. F. Bayen, M. Flato, C. Fronsdal, A. Lichnerovicz, D. Sternheimer, Deformation theory and quantization, Ann. Phys 111 (1978), 61-151 Zbl0377.53025
  3. L. Boutet de Monvel, V. Guillemin, The Spectral Theory of Toeplitz Operators, (1981), Princeton University Press, Princeton, NJ Zbl0469.47021MR620794
  4. L. Charles, Aspects semi-classiques de la quantification géométrique, (2000) 
  5. L. Charles, Spectral invariants of Toeplitz operators over symplectic two-dimensional orbifolds, (2002) 
  6. J. Duistermaat, The Heat Kernel Lefschetz Fixed Point Formula for the Spin-c Dirac Operator, (1996), Birkhäuser, Boston et al Zbl0858.58045MR1365745
  7. F. Faure, B. Zhilinskii, Qualitative features of intra-molecular dynamics. What can be learned from symmetry and topology?, Acta Applicandae Mathematicae 70 (2002), 265-282 Zbl1106.81305MR1892384
  8. B. Fedosov, A simple geometrical construction of deformation quantization, J. Differential Geom 40 (1994), 213-238 Zbl0812.53034MR1293654
  9. B. Fedosov, Deformation Quantization and Index Theory, (1995), Akademie-Verlag, Berlin Zbl0867.58061MR1389013
  10. B. Fedosov, On normal Darboux coordinates, Amer. Math. Soc. Transl 206 (2002), 81-93 Zbl1032.53065MR1939488
  11. B. Fedosov, On the trace density in deformation quantization, Deformation Quantization. Proceedings of the Meeting of Theoretical Physicist and Mathematicians (Strasbourg, 2001) (2002), 67-83, Walter de Gruyter, Berlin et al Zbl1014.53056
  12. B. Fedosov, On G-trace and G-index in deformation quantization, Lett. Math. Phys 52 (2000), 29-49 Zbl0998.53058MR1800489
  13. T. Kawasaki, The index of elliptic operators over V -manifolds, Nagoya Math. J 84 (1981), 135-157 Zbl0437.58020MR641150
  14. M. Pflaum, On the deformation quantization of symplectic orbispaces, (2003) Zbl1055.53069MR2013100
  15. M. Vergne, Equivariant index formula for orbifolds, Duke Math. J 82 (1996), 637-652 Zbl0874.57029MR1387687

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