Quasi-Hopf algebras associated with sl(2) and complex curves

We construct quasi-Hopf algebras quantizing double extensions of the Manin pairs of Drinfeld, associated to a curve with a meromorphic differential, a nd the Lie algebra sl(2). This construction makes use of an analysis of the vertex relations for the quantum groups obtained in our earlier work, PEW- type results and computation of R-matrices for them; its key step is a fact orization of the twist operator relating "conjugated" versions of these qua ntum groups.