We give an explicit construction of the trace on the algebra of quantum observables on a symplectiv orbifold and propose an index formula.
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.
@article{AIF_2004__54_5_1601_0, author = {Fedosov, Boris and Schulze, Bert-Wolfang and Tarkhanov, Nikolai}, title = {On the index theorem for symplectic orbifolds}, journal = {Annales de l'Institut Fourier}, pages = {1601--1639}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {54}, number = {5}, year = {2004}, doi = {10.5802/aif.2061}, mrnumber = {2127860}, zbl = {1071.53055}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.2061/} }
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 SP - 1601 EP - 1639 VL - 54 IS - 5 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.2061/ DO - 10.5802/aif.2061 LA - en ID - AIF_2004__54_5_1601_0 ER -
%0 Journal Article %A Fedosov, Boris %A Schulze, Bert-Wolfang %A Tarkhanov, Nikolai %T On the index theorem for symplectic orbifolds %J Annales de l'Institut Fourier %D 2004 %P 1601-1639 %V 54 %N 5 %I Association des Annales de l’institut Fourier %U http://archive.numdam.org/articles/10.5802/aif.2061/ %R 10.5802/aif.2061 %G en %F AIF_2004__54_5_1601_0
Fedosov, Boris; Schulze, Bert-Wolfang; Tarkhanov, Nikolai. On the index theorem for symplectic orbifolds. Annales de l'Institut Fourier, Volume 54 (2004) no. 5, pp. 1601-1639. doi : 10.5802/aif.2061. http://archive.numdam.org/articles/10.5802/aif.2061/
[1] Elliptic operators and compact groups, Lect. Notes Math 401, Springer-Verlag, 1974 | MR | Zbl
,[2] Deformation theory and quantization, Ann. Phys 111 (1978) p. 61-151 | Zbl
, , , & ,[3] The Spectral Theory of Toeplitz Operators, Princeton University Press, 1981 | MR | Zbl
& ,[4] Aspects semi-classiques de la quantification géométrique, Thèse, Université Paris IX - Dauphine, Paris, 2000
,[5] Spectral invariants of Toeplitz operators over symplectic two-dimensional orbifolds, Preprint, Università di Bologna, 2002
,[6] The Heat Kernel Lefschetz Fixed Point Formula for the Spin-c Dirac Operator, Birkhäuser, 1996 | MR | Zbl
,[7] 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] A simple geometrical construction of deformation quantization, J. Differential Geom 40 (1994) p. 213-238 | MR | Zbl
,[9] Deformation Quantization and Index Theory, Akademie-Verlag, 1995 | MR | Zbl
,[10] On normal Darboux coordinates, Amer. Math. Soc. Transl 206 (2002) no.2 p. 81-93 | MR | Zbl
,[11] On the trace density in deformation quantization, Walter de Gruyter, 2002, p. 67-83 | Zbl
,[12] On G-trace and G-index in deformation quantization, Lett. Math. Phys 52 (2000) p. 29-49 | MR | Zbl
,[13] The index of elliptic operators over -manifolds, Nagoya Math. J 84 (1981) p. 135-157 | MR | Zbl
,[14] On the deformation quantization of symplectic orbispaces, To appear in Differential Geometry and its Applications, 2003 | MR | Zbl
,[15] Equivariant index formula for orbifolds, Duke Math. J 82 (1996) p. 637-652 | MR | Zbl
,Cited by Sources: