The topological filtration of γ-structures

► We present enumerative results of γ-structures filtered by topological genus via symbolic methods. ► We derive the singularity analysis of a new bivariate generating function for γ-structures. ► Our results show a central limit theorem for the distribution of topological genus in γ-structures of given length. ► Our results are of relevance in the context of genus recursion and novel folding algorithms.