Homotopy Inner Products for Cyclic Operads

Details Homotopy Inner Products for Cyclic Operads Homotopy Inner Products for Cyclic Operads

2003-12-11

arxiv.org/abs/math/0312231v1

Mathematics

Algebraic Topology

33 pages

Scientific paper

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 Poincar\'e duality on the chain level of a suitable topological space is given.

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