We will discuss the BF theory on cobordisms endowed with cellular decompositions in BV-BFV formalism, its quantization and gluing properties. Partition functions are expressed in terms of the Reidemeister torsion and the propagator connecting the in- and out- boundary components, and also contain a mod 16 phase. As a side result we also obtain the gluing formula for propagators. This is a report on a joint work with A.S.Cattaneo and N.Reshetikhin.
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