3 problems

Let $H$ be a free abelian group, let $L'(H)$ be the free quasi-Lie algebra on $H$, and let $\mathcal A_k^t(H)$ be the abelian group generated by labelled planar binary trees of the…

Let $k$ be a positive integer, and consider the horizontal Whitney-tower sequence in which ${\sf K}^{\mu}_{4k-3}$ is the middle group. Let ${\sf L}'_{2k}$ denote the relevant degre…

Let ${\sf L}'_n$ be the degree-$n$ quasi-Lie algebra on generators $X_1,\ldots,X_m$, and let ${\sf D}'_n$ be the kernel of the bracketing map … Let $\mathcal T_n$ be the degree-$n$…