Abstract
This chapter discusses the reduced bar construction functorially on a deRham complex in a suitable way so that it may be paired with the cobar construction of a smooth chain complex. The associated Eilenberg–Moore spectral sequence of the reduced bar construction converges to the loop space cohomology in the simply connected case. Under reasonable conditions, the induced pairing for the Eilenberg–Moore spectral sequences are nondegenerate. The bar construction was originally used for chain complexes. This chapter also highlights a relation between Sullivan's minimal models and the reduced bar construction.
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