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,...,λn, 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 Zg=∑ni=1λg−1i, 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.