Toric varieties of Loday's associahedra and noncommutative cohomological field theories

Abstract : We introduce and study several new topological operads that should be regarded as nonsymmetric analogues of the operads of little 2-disks, framed little 2-disks, and Deligne-Mumford compactifications of moduli spaces of genus zero curves with marked points. These operads exhibit all the remarkable algebraic and geometric features that their classical analogues possess; in particular, it is possible to define a noncommutative analogue of the notion of cohomological field theory with similar Givental-type symmetries. This relies on rich geometry of the analogues of the Deligne-Mumford spaces, coming from the fact that they admit several equivalent interpretations: as the toric varieties of Loday's realisations of the associahedra, as the brick manifolds recently defined by Escobar, and as the De Concini-Procesi wonderful models for certain subspace arrangements.
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Contributor : Bruno Vallette <>
Submitted on : Monday, November 25, 2019 - 1:30:47 PM
Last modification on : Wednesday, November 27, 2019 - 1:38:20 AM

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Vladimir Dotsenko, Sergey Shadrin, Bruno Vallette. Toric varieties of Loday's associahedra and noncommutative cohomological field theories. Journal of topology, Oxford University Press, 2019, 12 (2), pp.463-535. ⟨10.03261⟩. ⟨hal-02378796⟩

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