Supersymmetry and cohomology of graph complexes. (English) Zbl 1410.14035
Summary: I describe a combinatorial construction of the cohomology classes in compactified moduli spaces of curves \(\widehat{Z}_{I}\in H^{*}\left(\bar{\mathcal{M}}_{g,n}\right)\) starting from the following data: \(\mathbb{Z}/2\mathbb{Z}\)-graded finite-dimensional associative algebra equipped with odd scalar product and an odd compatible derivation \(I\), whose square is nonzero in general, \(I^{2}\neq0\). As a byproduct I obtain a new combinatorial formula for products of \(\psi\)-classes, \(\psi_{i}=c_{1}\left(T_{p_{i}}^{*}\right)\), in the cohomology \(H^{*}\left(\bar{\mathcal{M}}_{g,n}\right)\).
MSC:
| 14J33 | Mirror symmetry (algebro-geometric aspects) |
| 53D37 | Symplectic aspects of mirror symmetry, homological mirror symmetry, and Fukaya category |
| 81Q30 | Feynman integrals and graphs; applications of algebraic topology and algebraic geometry |
| 05A15 | Exact enumeration problems, generating functions |
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