Office of Academic Resources
Chulalongkorn University
Chulalongkorn University

Home / Help

AuthorVaisman, Izu. author
TitleLectures on the Geometry of Poisson Manifolds [electronic resource] / by Izu Vaisman
ImprintBasel : Birkhรคuser Basel : Imprint: Birkhรคuser, 1994
Connect tohttp://dx.doi.org/10.1007/978-3-0348-8495-2
Descript VII, 206 p. online resource

CONTENT

0 Introduction -- 1 The Poisson bivector and the Schouten-Nijenhuis bracket -- 1.1 The Poisson bivector -- 1.2 The Schouten-Nijenhuis bracket -- 1.3 Coordinate expressions -- 1.4 The Koszul formula and applications -- 1.5 Miscellanea -- 2 The symplectic foliation of a Poisson manifold -- 2.1 General distributions and foliations -- 2.2 Involutivity and integrability -- 2.3 The case of Poisson manifolds -- 3 Examples of Poisson manifolds -- 3.1 Structures on ?n. Lie-Poisson structures -- 3.2 Dirac brackets -- 3.3 Further examples -- 4 Poisson calculus -- 4.1 The bracket of 1-forms -- 4.2 The contravariant exterior differentiations -- 4.3 The regular case -- 4.4 Cofoliations -- 4.5 Contravariant derivatives on vector bundles -- 4.6 More brackets -- 5 Poisson cohomology -- 5.1 Definition and general properties -- 5.2 Straightforward and inductive computations -- 5.3 The spectral sequence of Poisson cohomology -- 5.4 Poisson homology -- 6 An introduction to quantization -- 6.1 Prequantization -- 6.2 Quantization -- 6.3 Prequantization representations -- 6.4 Deformation quantization -- 7 Poisson morphisms, coinduced structures, reduction -- 7.1 Properties of Poisson mappings -- 7.2 Reduction of Poisson structures -- 7.3 Group actions and momenta -- 7.4 Group actions and reduction -- 8 Symplectic realizations of Poisson manifolds -- 8.1 Local symplectic realizations -- 8.2 Dual pairs of Poisson manifolds -- 8.3 Isotropic realizations -- 8.4 Isotropic realizations and nets -- 9 Realizations of Poisson manifolds by symplectic groupoids -- 9.1 Realizations of Lie-Poisson structures -- 9.2 The Lie groupoid and symplectic structures of T*G -- 9.3 General symplectic groupoids -- 9.4 Lie algebroids and the integrability of Poisson manifolds -- 9.5 Further integrability results -- 10 Poisson-Lie groups -- 10.1 Poisson-Lie and biinvariant structures on Lie groups -- 10.2 Characteristic properties of Poisson-Lie groups -- 10.3 The Lie algebra of a Poisson-Lie group -- 10.4 The Yang-Baxter equations -- 10.5 Manin triples -- 10.6 Actions and dressing transformations -- References


Mathematics Differential geometry Manifolds (Mathematics) Complex manifolds Physics Mathematics Differential Geometry Manifolds and Cell Complexes (incl. Diff.Topology) Theoretical Mathematical and Computational Physics



Location



Office of Academic Resources, Chulalongkorn University, Phayathai Rd. Pathumwan Bangkok 10330 Thailand

Contact Us

Tel. 0-2218-2929,
0-2218-2927 (Library Service)
0-2218-2903 (Administrative Division)
Fax. 0-2215-3617, 0-2218-2907

Social Network

  line

facebook   instragram