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.
Full text not available from this repository.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.
| Item Type: | Article |
|---|---|
| Journal or Publication Title: | Journal of the London Mathematical Society |
| Subjects: | Q Science > QA Mathematics |
| Departments: | Faculty of Science and Technology > Mathematics and Statistics |
| ID Code: | 59751 |
| Deposited By: | ep_importer_pure |
| Deposited On: | 02 Nov 2012 14:00 |
| Refereed?: | Yes |
| Published?: | Published |
| Last Modified: | 02 Nov 2012 14:00 |
| Identification Number: | |
| URI: | http://eprints.lancs.ac.uk/id/eprint/59751 |
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