Supersymmetry and cohomology of graph complexes

Serguei Barannikov

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4 Citations (SciVal)


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 languageEnglish
Pages (from-to)699-724
Number of pages26
JournalLetters in Mathematical Physics
Issue number3
Publication statusPublished - 4 Mar 2019
Externally publishedYes


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


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