Operads up to Homotopy and Deformations of Operad Maps

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dc.creatorvan der Laan, Pepijn P. I.
dc.date2002-08-06
dc.date.accessioned2026-07-07T04:50:04Z
dc.date.available2026-07-07T04:50:04Z
dc.descriptionFrom the `cofree' cooperad $T'(A[-1])$ on a collection $A$ together with a differential, we construct an $L_\infty$-algebra structure on the total space $\bigoplus_nA(n)$ that descends to coinvariants. We use this construction to define an $L_\infty$-algebra controlling deformations of the operad $P$ under $Q$ from a cofibrant resolution for an operad $Q$, and an operad map $Q\longrightarrow P$. Starting from a diffent cofibrant resolution one obtains a quasi isomorohic $L_\infty$-algebra. This approach unifies Markl's cotangent cohomology of operads and the approaches to deformation of $Q$-algebras by Balavoine, and Kontsevich and Soibelman.
dc.description26 pages
dc.identifierhttps://arxiv.org/abs/math/0208041
dc.identifierhttp://arxiv.org/abs/math/0208041
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/64666
dc.subjectQuantum Algebra
dc.subjectAlgebraic Topology
dc.subject18D50; 55U35
dc.titleOperads up to Homotopy and Deformations of Operad Maps
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