# Props of ribbon graphs, involutive Lie bialgebras and moduli spaces of curves M_g,n

@article{Merkulov2015PropsOR, title={Props of ribbon graphs, involutive Lie bialgebras and moduli spaces of curves M\_g,n}, author={Sergei A. Merkulov and Thomas Willwacher}, journal={arXiv: Quantum Algebra}, year={2015} }

We establish a new and surprisingly strong link between two previously unrelated theories: the theory of moduli spaces of curves Mg,n (which, according to Penner, is controlled by the ribbon graph complex) and the homotopy theory of Ed operads (controlled by ordinary graph complexes with no ribbon structure, introduced first by Kontsevich). The link between the two goes through a new intermediate stable ribbon graph complex which has roots in the deformation theory of quantum A∞ algebras and…

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