Every symplectic manifold (M^{2n}, ω) is locally symplectomorphic to (ℝ^{2n}, Σ dpᵢ∧dqᵢ). Consequence: no local invariants exist — all symplectic invariants are global, in sharp contrast to Riemannian geometry.
Every symplectic manifold (M^{2n}, ω) is locally symplectomorphic to (ℝ^{2n}, Σ dpᵢ∧dqᵢ). Consequence: no local invariants exist — all symplectic invariants are global, in sharp contrast to Riemannian geometry.