A universal A-infinity structure on Batalin-Vilkovisky algebras with multiple zeta value coefficients
arXiv:1501.02916
Abstract
We explicitly construct a universal A-infinity deformation of Batalin-Vilkovisky algebras, with all coefficients expressed as rational sums of multiple zeta values. If the Batalin-Vilkovisky algebra that we start with is cyclic, then so is the A-infinity deformation. Moreover, the adjoint action of the odd Poisson bracket acts by derivations of the A-infinity structure. The construction conjecturally defines a new presentation of the Grothendieck-Teichmueller Lie algebra.
The "regularization map'' from gravity chord diagrams to prime chord diagrams does not respect cooperadic compositions (it only does so on the associated graded for the filtration by number of residual chords). This commpletely undermines the main construction. Thanks to Anton Khoroshkin for raising the issue