Differential Geometry Working Seminar

Kain Dineen, University of Waterloo

Symplectic Capacities and Rigidity

As an application of Gromov's non-squeezing theorem, we'll prove that the symplectomorphisms (and anti-symplectomorphisms) of (ℝ^2m, 𝜔_0) are exactly the diffeomorphisms that additionally preserve the capacity of every compact ellipsoid. If time permits, then we will use this to prove that if a sequence of symplectomorphisms of any symplectic manifold (M, 𝜔) converges in the C^0-sense to a diffeomorphism 𝜓, then 𝜓*𝜔 = ± 𝜔.

MC 5479