## Abstract

We give an explicit formula for a quasi-isomorphism between the operads Hycomm (the homology of the moduli space of stable genus 0 curves) and BV/Δ (the homotopy quotient of Batalin-Vilkovisky operad by the BV-operator). In other words we derive an equivalence of Hycomm-algebras and BV-algebras enhanced with a homotopy that trivializes the BV-operator. These formulas are given in terms of the Givental graphs, and are proved in two different ways. One proof uses the Givental group action, and the other proof goes through a chain of explicit formulas on resolutions of Hycomm and BV. The second approach gives, in particular, a homological explanation of the Givental group action on Hycomm-algebras.

Original language | English |
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Pages (from-to) | 697-729 |

Number of pages | 33 |

Journal | Communications in Mathematical Physics |

Volume | 322 |

Issue number | 3 |

DOIs | |

State | Published - Sep 2013 |

Externally published | Yes |

## ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics