On the unfolding of folded symplectic structures

A folded symplectic structure is a closed 2-form which is nondegenerate exc ept on a hypersurface, and whose restriction to that hypersurface has maxim al rank. We show how a compact manifold equipped with a folded symplectic s tructure can sometimes be broken apart, or "unfolded", into honest compact symplectic orbifolds. A folded symplectic structure induces a spin-c structure which is canonical (up to homotopy). We describe how the index of the spin-c Dirac operator b ehaves with respect to unfolding.