We consider spin 1 2 free fermions on hyperelliptic Riemann surfaces including the infinite genus ones to study the configuration of the surfaces. The grand partition function of this system on the universal moduli space is defined using the branch point operator method. By taking a Coulomb gas analogy we observe a Kosterlitz-Thouless type phase transition on the universal moduli space which can be interpreted as the fusion and the condensation of handles. As a result, the notion of genus is lost. This is completely an analogy of a "thermodynamic" effect beyond the mathematical structure of the theory. Some remarks on the implication on string theories are also made. © 1991.
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