## Abstract

Semi-infinite forms on the moduli spaces of genus-zero Riemann surfaces with punctures and local coordinates are introduced. A partial operad of semi-infinite forms is constructed. Using semi-infinite forms and motivated by a partial suboperad of the partial operad of semi-infinite forms, topological vertex partial operads of type k < 0 and strong topological vertex partial operads of type k < 0 are constructed. It is proved that the category of (locally-)grading-restricted (strong) topological vertex operator algebras of type k < 0 and the category of (weakly) meromorphic ℤ x ℤ-graded algebras over the (strong) topological vertex partial operad of type k are isomorphic. As an application of this isomorphism theorem, the following conjecture of Lian-Zuckerman and Kimura-Voronov-Zuckerman is proved: A strong topological vertex operator algebra gives a (weak) homotopy Gerstenhaber algebra. These results hold in particular for the tensor product of the moonshine module vertex operator algebra, the vertex algebra constructed from a rank 2 Lorentz lattice and the ghost vertex operator algebra, studied in detail first by Lian and Zuckerman.

Original language | English (US) |
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Pages (from-to) | 191-241 |

Number of pages | 51 |

Journal | Communications in Contemporary Mathematics |

Volume | 2 |

Issue number | 2 |

State | Published - May 2000 |

## All Science Journal Classification (ASJC) codes

- General Mathematics
- Applied Mathematics