On the index theorem for symplectic orbifolds
[Sur le théorème de l'indice pour orbifoldes symplectiques]
Annales de l'Institut Fourier, Tome 54 (2004) no. 5, pp. 1601-1639.

Nous donnons une construction explicite de la trace sur l'algèbre des observables quantiques sur une orbifolde symplectique et proposons une formule de l'indice.

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

DOI : 10.5802/aif.2061
Classification : 53D55, 37J10
Fedosov, Boris 1 ; Schulze, Bert-Wolfang  ; Tarkhanov, Nikolai 1

1 Universität Potsdam, Institut für Mathematik, Postfach 60 15 53, 14415 Potsdam (Allemagne)
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Fedosov, Boris; Schulze, Bert-Wolfang; Tarkhanov, Nikolai. On the index theorem for symplectic orbifolds. Annales de l'Institut Fourier, Tome 54 (2004) no. 5, pp. 1601-1639. doi : 10.5802/aif.2061. http://www.numdam.org/articles/10.5802/aif.2061/

[1] M. F. Atiyah, Elliptic operators and compact groups, Lect. Notes Math 401, Springer-Verlag, 1974 | MR | Zbl

[2] F. Bayen, M. Flato, C. Fronsdal, A. Lichnerovicz & D. Sternheimer, Deformation theory and quantization, Ann. Phys 111 (1978) p. 61-151 | Zbl

[3] L. Boutet De Monvel & V. Guillemin, The Spectral Theory of Toeplitz Operators, Princeton University Press, 1981 | MR | Zbl

[4] L. Charles, Aspects semi-classiques de la quantification géométrique, Thèse, Université Paris IX - Dauphine, Paris, 2000

[5] L. Charles, Spectral invariants of Toeplitz operators over symplectic two-dimensional orbifolds, Preprint, Università di Bologna, 2002

[6] J. Duistermaat, The Heat Kernel Lefschetz Fixed Point Formula for the Spin-c Dirac Operator, Birkhäuser, 1996 | MR | Zbl

[7] F. Faure & B. Zhilinskii, Qualitative features of intra-molecular dynamics. What can be learned from symmetry and topology?, Acta Applicandae Mathematicae 70 (2002) p. 265-282 | MR | Zbl

[8] B. Fedosov, A simple geometrical construction of deformation quantization, J. Differential Geom 40 (1994) p. 213-238 | MR | Zbl

[9] B. Fedosov, Deformation Quantization and Index Theory, Akademie-Verlag, 1995 | MR | Zbl

[10] B. Fedosov, On normal Darboux coordinates, Amer. Math. Soc. Transl 206 (2002) no.2 p. 81-93 | MR | Zbl

[11] B. Fedosov, On the trace density in deformation quantization, Walter de Gruyter, 2002, p. 67-83 | Zbl

[12] B. Fedosov, On G-trace and G-index in deformation quantization, Lett. Math. Phys 52 (2000) p. 29-49 | MR | Zbl

[13] T. Kawasaki, The index of elliptic operators over V-manifolds, Nagoya Math. J 84 (1981) p. 135-157 | MR | Zbl

[14] M. Pflaum, On the deformation quantization of symplectic orbispaces, To appear in Differential Geometry and its Applications, 2003 | MR | Zbl

[15] M. Vergne, Equivariant index formula for orbifolds, Duke Math. J 82 (1996) p. 637-652 | MR | Zbl

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