Feynman diagrams and minimal models for operadic algebras
- Autores: J. Chuang, A. Lazarev
- Localización: Journal of the London Mathematical Society, ISSN 0024-6107, Vol. 81, Nº 2, 2010, págs. 317-337
- Idioma: inglés
- DOI: 10.1112/jlms/jdp073
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Resumen
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�fs �edual construction�f producing graph cohomology classes from contractible differential graded Frobenius algebras.
