SL(2,C) Topological Quantum Field Theory with Corners

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The paper contains the construction of a topological quantum field theory in which gluings along surfaces with boundary are allowed. The construction is made by using quantum deformations of sl(2,C). In the construction there appears a sign obstruction to some of the Moore-Seiberg equations. This problem is solved by means of the Klein four group.
LATEX, 70 figures

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