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Book DetailsContemporary MathematicsVolume: 450; 2008; 311 ppMSC: Primary 53; 19; 58; 81; 14; 22; 47;
This volume is a collection of articles by speakers at the conference “Poisson 2006: Poisson Geometry in Mathematics and Physics”, which was held June 5–9, 2006, in Tokyo, Japan. Poisson 2006 was the fifth in a series of international conferences on Poisson geometry that are held once every two years. The aim of these conferences is to bring together mathematicians and mathematical physicists who work in diverse areas but have common interests in Poisson geometry. The program for Poisson 2006 was remarkable for the overlap of topics that included deformation quantization, generalized complex structures, differentiable stacks, normal forms, and groupvalued moment maps and reduction. The articles represent current research in Poisson geometry and should be valuable to anyone interested in Poisson geometry, symplectic geometry, and mathematical physics. This volume also contains lectures by the principal speakers of the threeday school held at Keio University that preceded Poisson 2006.
ReadershipGraduate students and research mathematicians interested in Symplectic and Poisson geometry, deformation quantization, and mathematical physics.

Table of Contents

Articles

Pierre Bieliavsky, Laurent Claessens, Daniel Sternheimer and Yannick Voglaire  Quantized anti de Sitter spaces and nonformal deformation quantizations of symplectic symmetric spaces [ MR 2397616 ]

Christian Blohmann and Alan Weinstein  Grouplike objects in Poisson geometry and algebra [ MR 2397617 ]

Olivier Brahic and Rui Loja Fernandes  Poisson fibrations and fibered symplectic groupoids [ MR 2397618 ]

Henrique Bursztyn, Gil R. Cavalcanti and Marco Gualtieri  Generalized Kähler and hyperKähler quotients [ MR 2397619 ]

Alberto S. Cattaneo  Deformation quantization and reduction [ MR 2397620 ]

JeanPaul Dufour  Examples of higher order stable singularities of Poisson structures [ MR 2397621 ]

François GayBalmaz and Tudor S. Ratiu  Poisson reduction and the Hamiltonian structure of the EulerYangMills equations [ MR 2397622 ]

Tara S. Holm  Orbifold cohomology of abelian symplectic reductions and the case of weighted projective spaces [ MR 2397623 ]

Noriaki Ikeda  Deformation of graded Poisson (BatalinVilkovisky) structures [ MR 2397624 ]

Alexander V. Karabegov  Deformation quantization of a KählerPoisson structure vanishing on a Levi nondegenerate hypersurface [ MR 2397625 ]

JiangHua Lu  A note on Poisson homogeneous spaces [ MR 2397626 ]

E. Meinrenken  Lectures on pure spinors and moment maps [ MR 2397627 ]

S. A. Merkulov  Lectures on PROPs, Poisson geometry and deformation quantization [ MR 2397628 ]

Pierre Schapira  Deformation quantization modules on complex symplectic manifolds [ MR 2397629 ]

Michel Van den Bergh  Noncommutative quasiHamiltonian spaces [ MR 2397630 ]

Stefan Waldmann  Locally noncommutative spacetimes [ MR 2397631 ]


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This volume is a collection of articles by speakers at the conference “Poisson 2006: Poisson Geometry in Mathematics and Physics”, which was held June 5–9, 2006, in Tokyo, Japan. Poisson 2006 was the fifth in a series of international conferences on Poisson geometry that are held once every two years. The aim of these conferences is to bring together mathematicians and mathematical physicists who work in diverse areas but have common interests in Poisson geometry. The program for Poisson 2006 was remarkable for the overlap of topics that included deformation quantization, generalized complex structures, differentiable stacks, normal forms, and groupvalued moment maps and reduction. The articles represent current research in Poisson geometry and should be valuable to anyone interested in Poisson geometry, symplectic geometry, and mathematical physics. This volume also contains lectures by the principal speakers of the threeday school held at Keio University that preceded Poisson 2006.
Graduate students and research mathematicians interested in Symplectic and Poisson geometry, deformation quantization, and mathematical physics.

Articles

Pierre Bieliavsky, Laurent Claessens, Daniel Sternheimer and Yannick Voglaire  Quantized anti de Sitter spaces and nonformal deformation quantizations of symplectic symmetric spaces [ MR 2397616 ]

Christian Blohmann and Alan Weinstein  Grouplike objects in Poisson geometry and algebra [ MR 2397617 ]

Olivier Brahic and Rui Loja Fernandes  Poisson fibrations and fibered symplectic groupoids [ MR 2397618 ]

Henrique Bursztyn, Gil R. Cavalcanti and Marco Gualtieri  Generalized Kähler and hyperKähler quotients [ MR 2397619 ]

Alberto S. Cattaneo  Deformation quantization and reduction [ MR 2397620 ]

JeanPaul Dufour  Examples of higher order stable singularities of Poisson structures [ MR 2397621 ]

François GayBalmaz and Tudor S. Ratiu  Poisson reduction and the Hamiltonian structure of the EulerYangMills equations [ MR 2397622 ]

Tara S. Holm  Orbifold cohomology of abelian symplectic reductions and the case of weighted projective spaces [ MR 2397623 ]

Noriaki Ikeda  Deformation of graded Poisson (BatalinVilkovisky) structures [ MR 2397624 ]

Alexander V. Karabegov  Deformation quantization of a KählerPoisson structure vanishing on a Levi nondegenerate hypersurface [ MR 2397625 ]

JiangHua Lu  A note on Poisson homogeneous spaces [ MR 2397626 ]

E. Meinrenken  Lectures on pure spinors and moment maps [ MR 2397627 ]

S. A. Merkulov  Lectures on PROPs, Poisson geometry and deformation quantization [ MR 2397628 ]

Pierre Schapira  Deformation quantization modules on complex symplectic manifolds [ MR 2397629 ]

Michel Van den Bergh  Noncommutative quasiHamiltonian spaces [ MR 2397630 ]

Stefan Waldmann  Locally noncommutative spacetimes [ MR 2397631 ]