The Symplectic Camel · non-squeezing

Gromov (1985): if B⁴(r) embeds symplectically in Z(R) = B²(R) × ℝ², then r ≤ R.

x₁ y₁ x₂

Scene 1 of 4

Volume-preserving squeeze

4-volume kept symplectic fits the hole

y₂ = −r+r

outside the cylinder

cylinder wall, radius R

Deform 0.00 Hole R / r 0.72 drag to orbit · scroll to zoom · space to pause