  We compute the structure constants of topological symmetric orbifold theories
up to third order in the large N expansion. The leading order structure
constants are dominated by topological metric contractions. The first order
interactions are single cycles joining while at second order we can have double
joining as well as splitting. At third order, single cycle joining obtains
genus one contributions. We also compute illustrative small N structure
constants. Our analysis applies to all second quantized Frobenius algebras, a
large class of algebras that includes the cohomology ring of the Hilbert scheme
of points on K3 among many others. We point out interesting open questions that
our results raise.
