  A projected Gromov-Witten variety is the union of all rational curves of
fixed degree that meet two opposite Schubert varieties in a homogeneous space X
= G/P. When X is cominuscule we prove that the map from a related Gromov-Witten
variety is cohomologically trivial. This implies that all (3 point, genus zero)
K-theoretic Gromov-Witten invariants of X are determined by the projected
Gromov-Witten varieties, which extends an earlier result of Knutson, Lam, and
Speyer. Our proof uses that any projected Gromov-Witten variety in a
cominuscule space is also a projected Richardson variety.
