Linear symplectic geometry

The second chapter introduces the basic concepts of symplectic topology in the linear algebra setting, such as symplectic vector spaces, the linear symplectic group, Lagrangian subspaces, and the Maslov index. In the section on linear complex structures particular emphasis is placed on the homotopy equivalence between the space of symplectic forms and the space of linear complex structures. The chapter includes sections on symplectic vector bundles and the first Chern class.