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.

## 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 |
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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: | 07 Jan 2015 18:02 |

Identification Number: | |

URI: | http://eprints.lancs.ac.uk/id/eprint/59751 |

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