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This is a Quantitative Study study.

October 20, 2025Open Access

A complex of ribbon quivers and M₆, ₌

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This analysis shows how cohomology computes the structure of the moduli space of algebraic curves, implying implications for dg Lie algebras.

The complex $ ext{ORGC}_d^{(g,m)}$ computes compactly supported cohomology of the moduli space $ ext{M}_{g,m}$.
For $d ext{ ≤ 2}$, the zero-th cohomology group indicates limited homotopy non-trivial automorphisms.
A natural dg Lie algebra structure governs the deformation theory of degree $d$ pre-Calabi-Yau algebras.
A subspace of $H^1( ext{Der}( ext{P}re ext{CY}_2))$ is isomorphic to the Grothendieck-Teichmüller Lie algebra.

Sergei Merkulov (2025) studied this question.

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This analysis shows how cohomology computes the structure of the moduli space of algebraic curves, implying implications for dg Lie algebras.