Abstract
A positive, diffeomorphism-invariant generalized measure on the space of metrics of a two-dimensional smooth manifold is constructed. We use the term generalized measure analogously with the generalized measures of Ashtekar and Lewandowski and of Baez. A family of actions is presented which, when integrated against this measure gives the two-dimensional axiomatic topological quantum field theories, or TQFTs, in terms of which Durhuus and Jonsson decompose every two-dimensional unitary TQFT as a direct sum.
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