A Brief Introduction to Symplectic and Contact Manifolds

The book introduces the basic notions in Symplectic and Contact Geometry at the level of the second year graduate student. It also contains many exercises, some of which are solved only in the last chapter.

We begin with the linear theory, then give the definition of symplectic manifolds and some basic examples, review advanced calculus, discuss Hamiltonian systems, tour rapidly group and the basics of contact geometry, and solve problems in chapter 8. The material just described can be used as a one semester course on Symplectic and Contact Geometry.

The book contains also more advanced material, suitable to advanced graduate students and researchers.

Contents:

• Symplectic Vector Spaces
• Symplectic Manifolds
• Hamiltonian Systems and Poisson Algebra
• Group Actions
• Contact Manifolds
• Solutions of Selected Exercises
• Epilogue: The C0-Symplectic and Contact Topology

Readership: Graduate students, researchers and more advanced mathematicians.
Key Features:

• It is brief
• The easy part has been tested and been used for a short course
• The advanced material develops things related to one of the author's research further
• There is no book, going from the very elementary part to the very advanced level, like this one