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The A-infinity operad and the moduli space of curves

Kevin Costello
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Abstract

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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Kevin Costello. 2004-09-15. The A-infinity operad and the moduli space of curves. https://arxiv.org/abs/math/0402015

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