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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

The A-infinity operad and the moduli space of curves

classification math.AG math.QA
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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  1. Calabi-Yau Deformation Quantization

    math.QA 2026-07 conditional novelty 3.0

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