Lectures on Poisson Geometry (Geometry and Topology Monographs, Vol. 17)

Finally, “Lectures on Poisson Geometry”, which is a collection of lectures on various aspects of Poisson geometry, edited by T. Ratiu, A. Weinstein, and myself, has appeared as Volume 17 of the series Geometry and Topology Monographs:


Poisson geometry is a rapidly growing subject,
with many interactions and applications in areas of mathematics
and physics, such as classical differential geometry, Lie theory,
noncommutative geometry, integrable systems, fluid dynamics, quantum
mechanics, and quantum field theory. Recognizing the role played by
Poisson geometry and the significant research it has generated, the
Abdus Salam International Centre for Theoretical Physics in Trieste,
Italy, sponsored a 3–week summer activity on this subject (July 4–22
2005) in order to bring it to the attention of scientists and students
from developing countries. There was an overwhelming response to this
program, which brought together more than 150 participants from all over
the world with varied backgrounds, from graduate students to experts.

The program consisted of a two-week intensive school
comprising 10 minicourses, followed by a week-long international research
conference. The lecturers at the school were asked to turn their notes
into sections of a book that could serve as a quick introduction to the
current state of research in Poisson geometry. We hope that the present
volume will be  useful to people who want to learn about Poisson geometry
and its applications.


Lectures on integrability of Lie brackets 1
Marius Crainic and Rui Fernandes

Normal forms of Poisson structures 109
Jean-Paul Dufour and Tien Zung Nguyen

Deformation quantisation of Poisson manifolds 171
Simone Gutt

Applications of Poisson geometry to physical problems 221
Darryl D Holm

Hamiltonian and quantum mechanics 385
Anatol Odzijewicz

Lectures on Poisson groupoids 473
Camille Laurent-Gengoux, Mathieu Stiénon and Ping Xu

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