Chuang, J. & Lazarev, A. (2010). Feynman diagrams and minimal models for operadic algebras. Journal of the London Mathematical Society, 81(2), pp. 317337. doi: 10.1112/jlms/jdp073

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Abstract
We construct an explicit minimal model for an algebra over the cobarconstruction 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 wellknown 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 byproduct of our work we prove gaugeindependence of Kontsevich's ‘dual construction’ producing graph cohomology classes from contractible differential graded Frobenius algebras.
Item Type:  Article 

Uncontrolled Keywords:  STRING FIELDTHEORY, HOMOTOPY ALGEBRAS 
Subjects:  Q Science > QA Mathematics Q Science > QC Physics 
Divisions:  School of Engineering & Mathematical Sciences > Department of Mathematical Science 
URI:  http://openaccess.city.ac.uk/id/eprint/187 
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