Independent Loop Invariants for 2+1 Gravity

We identify an explicit set of complete and independent Wilson loop invariants for 2+1 gravity on a three-manifold $M=\R\timesΣ^g$, with $Σ^g$ a compact oriented Riemann surface of arbitrary genus $g$. In the derivation we make use of a global cross section of the $PSU(1,1)$-principal bundle over Teichmüller space given in terms of Fenchel-Nielsen coordinates.

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