A mod-2 intersection invariant detects nontrivial loops of embedded 2-spheres in S^2×S^2 and connected sums that evade all light-bulb moves.
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Pseudo-Isotopy and Diffeomorphisms of the 4-Sphere I: Loops of Spheres
A mod-2 intersection invariant detects nontrivial loops of embedded 2-spheres in S^2×S^2 and connected sums that evade all light-bulb moves.