  In this paper we study the effect of a torus topology on Loop Quantum
Cosmology. We first derive the Teichmueller space parametrizing all possible
tori using Thurston's theorem and construct a Hamiltonian describing the
dynamics of these torus universes. We then compute the Ashtekar variables for a
slightly simplified torus such that the Gauss constraint can be solved easily.
We perform a canonical transformation so that the holomies along the edges of
the torus reduce to a product between almost and strictly periodic functions of
the new variables. The drawback of this transformation is that the components
of the densitized triad become complicated functions of these variables.
Nevertheless we find two ways of quantizing these components, which in both
cases leads surprisingly to a continuous spectrum.
