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The A-infinity operad and the moduli space of curves

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arxiv math/0402015 v2 pith:FF5NYERE submitted 2004-02-02 math.AG math.QA

Kevin Costello This is my paper · ORCID
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keywords operadmodularmodulia-infinitycurvescyclicenvelopespace
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The modular envelope of a cyclic operad is the smallest modular operad containing it. A modular operad is constructed from moduli spaces of Riemann surfaces with boundary; this modular operad is shown to be the modular envelope of the A-infinity cyclic operad. This gives a new proof of the result of Harer-Mumford-Thurston-Penner-Kontsevich that a cell complex built from ribbon graphs is homotopy equivalent to the moduli space of curves.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. The Construction of Correlators in Finite Rigid Logarithmic Conformal Field Theory

    math.QA 2025-07 conditional novelty 8.0 of 10

    For any non-semisimple modular category, special symmetric Frobenius algebras now give all consistent open-closed correlators, with a holographic description and a Batalin-Vilkovisky structure on local operators.

  2. Reflection Equivariance and the Heisenberg Picture for Spaces of Conformal Blocks

    math.QA 2025-07 accept novelty 7.0 of 10

    Orientation reversal of surfaces corresponds algebraically to the modified trace, and reflection equivariant modular functors are exactly those whose circle category is modular and whose conformal blocks are the uniqu...

  3. Calabi-Yau Deformation Quantization

    math.QA 2026-07 conditional novelty 3.0 of 10

    A Calabi-Yau version of Kontsevich's formality morphism is recorded, yielding canonical closed deformation quantizations for unimodular holomorphic Poisson Calabi-Yau manifolds.

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