Quantitative symplectic geometry [article]

K.Cieliebak, H.Hofer, J.Latschev, F.Schlenk
2005 arXiv   pre-print
While symplectic manifolds have no local invariants, they do admit many global numerical invariants. Prominent among them are the so-called symplectic capacities. Different capacities are defined in different ways, and so relations between capacities often lead to surprising relations between different aspects of symplectic geometry and Hamiltonian dynamics. In this paper we present an attempt to better understand the space of all symplectic capacities, and discuss some further general
more » ... s of symplectic capacities. We also describe several new relations between certain symplectic capacities on ellipsoids and polydiscs. Throughout the discussion we mention many open problems.
arXiv:math/0506191v1 fatcat:5plrjwxrtreo5lsrvv2yo6nv6y