  We consider the folding of a self-avoiding homopolymer on a lattice, with
saturating hydrogen bond interactions. Our goal is to numerically evaluate the
statistical distribution of the topological genus of pseudoknotted
configurations. The genus has been recently proposed for classifying
pseudoknots (and their topological complexity) in the context of RNA folding.
We compare our results on the distribution of the genus of pseudoknots, with
the theoretical predictions of an existing combinatorial model for an
infinitely flexible and stretchable homopolymer. We thus obtain that steric and
geometric constraints considerably limit the topological complexity of
pseudoknotted configurations, as it occurs for instance in real RNA molecules.
We also analyze the scaling properties at large homopolymer length, and the
genus distributions above and below the critical temperature between the
swollen phase and the compact-globule phase, both in two and three dimensions.
