2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/152059We show that Tolman's example (of a six dimensional Hamiltonian $T^2$-space with isolated fixed points and no compatible Kähler structure) can be constructed from the flag variety $U(3)/U(1)^3$ by $U(2)$-equivariant symplectic surgery. This implies that Tolman's space has a ``transversal multiplicity-free'' action of $U(2)$ and that Delzant's theorem ``every compact multiplicity-free torus action is Kähler'' \cite{D1} does not generalize to non-abelian actions.LaTeX using epic, eepic. 10 pages, 4 figuresDifferential Geometrytext