Poly-symplectic geometry and the AKSZ formalism

Symplectic Geometry

1 Symplectic Manifolds 5 1.1 Symplectic Linear Algebra . . . . . . . . . . . . . . . . . . . . . . . 5 1.2 Symplectic Forms . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.3 Cotangent Bundles . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.4 Moser’s Trick . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.5 Darboux and Moser Theorems . . . . . . . . . . . . . . . ....

Symplectic Geometry

Symplectic Geometry

Symplectic Geometry

These notes are written for a ten week graduate class on symplectic geometry. Most of the material here is included in Michèle Audin’s book Torus actions on symplectic manifolds, which I used heavily in preparing these notes. There are a few topics that we cover that are not in Audin’s book, such as polygon spaces, cohomology of flag manifolds, and CS/GKM theory. More significant, however, are ...

Symplectic Geometry