Abstract
In this work we discuss the construction of “simplicial BF theory”, the field theory with finite-dimensional space of fields, associated to a triangulated manifold, that is in a sense equivalent to topological BF theory on the manifold (with infinitedimensional space of fields). This is done in framework of simplicial program — program of constructing discrete topological field theories. We also discuss the relation of these constructions to homotopy algebra.
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