## Abstract

I describe a combinatorial construction of the cohomology classes in compactified moduli spaces of curves Z^ _{I} ∈ H ^{∗} (M¯ _{g} _{,} _{n} ) starting from the following data: Z/ 2 Z-graded finite-dimensional associative algebra equipped with odd scalar product and an odd compatible derivation I, whose square is nonzero in general, I ^{2} ≠ 0. As a byproduct I obtain a new combinatorial formula for products of ψ-classes, ψi=c1(Tpi∗), in the cohomology H ^{∗} (M¯ _{g} _{,} _{n} ).

Original language | English |
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Pages (from-to) | 699-724 |

Number of pages | 26 |

Journal | Letters in Mathematical Physics |

Volume | 109 |

Issue number | 3 |

DOIs | |

Publication status | Published - 4 Mar 2019 |

Externally published | Yes |

## Keywords

- Graph complexes
- Gromov–Witten invariants
- Mirror symmetry
- Moduli spaces