Coisotropic rigidity and C0-symplectic geometry

Symplectic torus actions with coisotropic principal orbits

In this paper we completely classify symplectic actions of a torus T on a compact connected symplectic manifold (M, σ) when some, hence every, principal orbit is a coisotropic submanifold of (M, σ). That is, we construct an explicit model, defined in terms of certain invariants, of the manifold, the torus action and the symplectic form. The invariants are invariants of the topology of the manif...

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 Rigidity for Anosov Hypersurfaces

There is a canonical exact symplectic structure on the unit tangent bundle of a Riemannian manifold M given by pulling-back the symplectic two form ω and Liouville one form λ from the cotangent bundle T ∗M using the Riemannian metric. The pull-back of λ gives a contact form on level-sets of the length function on TM . The geodesic flow of M is given by the Reeb vectorfield of this contact struc...

Symplectic Geometry