Chuang, Joseph and Lazarev, Andrey (2010) Feynman diagrams and minimal models for operadic algebras. Journal of the London Mathematical Society, 81 (2). pp. 317-337. ISSN 1469-7750Full text not available from this repository.
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.
|Journal or Publication Title:||Journal of the London Mathematical Society|
|Subjects:||Q Science > QA Mathematics|
|Departments:||Faculty of Science and Technology > Mathematics and Statistics|
|Deposited On:||02 Nov 2012 14:00|
|Last Modified:||14 Apr 2016 01:22|
Actions (login required)