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• W3122706084 abstract "We construct an explicit minimal model for an algebra over the cobar-construction of a differential graded operad. The structure maps of this minimal model are expressed in terms of sums over decorated trees. We introduce the appropriate notion of a homotopy equivalence of operadic algebras and show that our minimal model is homotopy equivalent to the original algebra. All this generalizes and gives a conceptual explanation of well-known results for A∞-algebras. Furthermore, we show that these results carry over to the case of algebras over modular operads; the sums over trees get replaced by sums over general Feynman graphs. As a by-product of our work we prove gauge-independence of Kontsevich's ‘dual construction’ producing graph cohomology classes from contractible differential graded Frobenius algebras." @default.
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• W3122706084 date "2010-01-13" @default.
• W3122706084 modified "2023-10-14" @default.
• W3122706084 title "Feynman diagrams and minimal models for operadic algebras" @default.
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• W3122706084 doi "https://doi.org/10.1112/jlms/jdp073" @default.
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