Cohomology of parallelized n-manifolds carries a natural homotopy involutive n-Frobenius structure extending the rational homotopy type, via Quillen equivalence to n-Poisson cooperad comodules.
A Koszul duality for props
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abstract
The notion of prop models the operations with multiple inputs and multiple outpus, acting on some algebraic structures like the bialgebras or the Lie bialgebras. In this paper, we generalize the Koszul duality theory of associative algebras and operads to props.
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Homotopy Frobenius structures on the cohomology of a manifold
Cohomology of parallelized n-manifolds carries a natural homotopy involutive n-Frobenius structure extending the rational homotopy type, via Quillen equivalence to n-Poisson cooperad comodules.