  The partition function of Euclidean Yang-Mills theory on two dimensional
surfaces is given by the Migdal formula. It involves the area and topological
characteristics of the surface. We consider this theory on a class of infinite
genus surfaces that are constructed recursively. We make use of this recursive
structure to compute the partition functions (with or without additional Wilson
loops) on such surfaces. Our method also works for the quantum deformed
Yang-Mills theory.
