2 problems

Let $M_{n}^{J}$ be the degree-$n$ piece at filtration level $J$, let $\mathrm{wt}(\omega)$ denote the weight of $\omega$, and let $d_{\sim}$ be the indicated component of the differ…

Let $Y$ be a $c$-step nilpotent space, and let $\operatorname{V\delta}^{n}_{Y}(L)$ denote its volume of nullhomotopies in degree $n$ at scale $L$. General nilpotent upper-bound con…