Isotropic isotopy and symplectic null sets.
Capacity is an important numerical invariant of symplectic manifolds. This paper studies when a subset of a symplectic manifold is null, i.e., can be removed without affecting the ambient capacity. After examples of open null sets and codimension-2 non-null sets, geometric techniques are developed to perturb any isotopy of a loop to a hamiltonian flow; it follows that sets of dimension 0 and 1 are null. For isotropic sets of higher dimensions, obstructions to the perturbation are found in homotopy groups of the orthogonal groups.
Tokieda
T F
TF
Department of Mathematics, McGill University, 805 Sherbrooke Street West, Montreal, PQ H3A 2K6, Canada.