  We prove that in dimension 4 the Gromov non-squeezing phenomenon is
persistent with respect to $C ^{0}$ symplectic perturbations of the symplectic
form on the range. This motivates an intriguing question on further deforming
non-squeezing to general nearby forms. Our methods consist of a certain trap
idea for holomorphic curves, analogous to traps in dynamical systems, and
Hofer-Wysocki-Zehnder polyfold regularization in Gromov-Witten theory,
especially as recently worked out in this present context by the team of
Franziska Beckschulte, Ipsita Datta, Irene Seifert, Anna-Maria Vocke, and
Katrin Wehrheim.
