Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1994-05-26
Symposia Gaussiana, Proc. of the 2nd Gauss Symposium, Munich, 1993, Conf. A (Berlin, New York), Walter de ruyter, 1995, pp. 52
Physics
High Energy Physics
High Energy Physics - Theory
51 pages, close to published version
Scientific paper
A category N of labeled (oriented) trivalent graphs (nets) or ribbon graphs is extended by new generators called fusing, braiding, twist and switch with relations which can be called Moore--Seiberg relations. A functor to N is constructed from the category Surf of oriented surfaces with labeled boundary and their homeomorphisms. Given an (eventually non-semisimple) k-linear abelian ribbon braided category C with some finiteness conditions we construct a functor from a central extension of N with the set of labels ObC to k-vector spaces. Composing the functors we get a modular functor from a central extension of Surf to k-vector spaces. This is a mathematical paper which explains how to get proofs for its hep-th companion paper, which should be read first. Complete proofs are not given here. (Talk at Second Gauss Simposium, Munich, August 1993.)
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