Abstract
Cohomological field theories are defined and investigated in an approach that begins with a cohomological theory on the (usually trivial) space of all field configurations and then imposes constraints and gauge fixing to restrict to a subspace such as a moduli space. This approach makes manifest the connection between the language of field theory and the topology, and implies that all cohomological information about the subspace is encoded in the cohomological theory. Derivations of lagrangians are also simplified. Cohomological Yang-Mills and cohomological gravity are examined from this perspective, a derivation of world-sheet Feynman rules for cohomological gravity is outlined.
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