Homotopy Inner Products for Cyclic Operads

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dc.creatorLongoni, Riccardo
dc.creatorTradler, Thomas
dc.date2003-12-11
dc.date.accessioned2026-07-07T05:03:48Z
dc.date.available2026-07-07T05:03:48Z
dc.descriptionWe 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.
dc.description33 pages
dc.identifierhttps://arxiv.org/abs/math/0312231
dc.identifierhttp://arxiv.org/abs/math/0312231
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/69562
dc.subjectAlgebraic Topology
dc.subject55P48; 18D50
dc.titleHomotopy Inner Products for Cyclic Operads
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