Homotopy Inner Products for Cyclic Operads

Riccardo Longoni; Thomas Tradler

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Homotopy Inner Products for Cyclic Operads

Riccardo Longoni·Thomas Tradler

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Abstract

We introduce the notion of homotopy inner products for any cyclic quadratic Koszul operad $\mathcal O$, generalizing the construction already known for the associative operad. This is done by defining a colored operad $\hat{\mathcal O}$, which describes modules over $\mathcal O$ with invariant inner products. We show that $\hat{\mathcal O}$ satisfies Koszulness and identify algebras over a resolution of $\hat{\mathcal O}$ in terms of derivations and module maps. An application to Poincaré duality on the chain level of a suitable topological space is given.

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Riccardo Longoni, Thomas Tradler. 2003-12-11. Homotopy Inner Products for Cyclic Operads. https://arxiv.org/abs/math/0312231

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