The imploded cross-section of a Hamiltonian K-space is a stratified space, each of whose strata is symplectic. This construction remedies the fact that although the preimage of the interior of the fundamental Weyl group under the moment map for a Hamiltonian K-action is a symplectic T-space (where T is the maximal torus of K), the preimage of the Lie algebra of the maximal torus is not.

The universal imploded cross-section is the imploded cross-section of the cotangent bundle. We compute the intersection cohomology of the universal imploded cross-section of SU(3), and show that it is different from the intersection cohomology of a point.

Coauthor: Nan-Kuo Ho