Quantitative symplectic geometry
Symplectic Geometry
2007-05-23 v1 Differential Geometry
Abstract
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 properties 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.
Cite
@article{arxiv.math/0506191,
title = {Quantitative symplectic geometry},
author = {K. Cieliebak and H. Hofer and J. Latschev and F. Schlenk},
journal= {arXiv preprint arXiv:math/0506191},
year = {2007}
}
Comments
43 pages, 3 figures