3 problems

Higher-dimensional recovery conjecture. A similar procedure can be used to recover cycles in higher dimensions.

Lifted toroidal-cycle conjecture. All cycles in $K$ which are trivial in $G$ can be written in terms of lifts of toroidal cycles.

Let $G$ be a digraph. Write $H_*^{\operatorname{cell}}(G;\mathbb R)$ for its cellular homology and $H_*^c(G;\mathbb R)$ for its singular cubical homology. The cellular–singular cub…