3 problems

Consider the universal map $\Phi_{{\text{\rm\tiny geo}}}^{\mathrm{Novikov}}$ induced by $\Phi_{{\text{\rm\tiny geo}}}$ after taking the operad quotient … in the construction given…

Let $\operatorname{PreLie}$ be the PreLie operad, let $\operatorname{CycLie}$ be the cyclic Lie module, and let $M$ be the sub-operad generated by the image of…

Let $\operatorname{PreLie}$ be the PreLie operad and let $M$ be the sub-operad generated by the image of $\operatorname{CycLie}$ under the injective map $\lambda$. The composition…