Classification and construction of unitary topological field theories in two dimensions

It is proven that unitary two-dimensional topological field theories are uniquely characterized by n positive real numbers λ₁ ,...,λ_n, which can be regarded as the eigenvalues of a Hermitian handle creation operator. The number n is the dimension of the Hilbert space associated with the circle, and the partition functions for closed surfaces have the form Z_g=Σ_i=1ⁿλ _i^g-1, where g is the genus. The eigenvalues can be arbitrary positive numbers. It is shown how such a theory can be constructed on triangulated surfaces.