9 problems

Let $\Gamma$ be a planar graph, and let $B_n\Gamma$ and $P B_n\Gamma$ denote its $n$-strand braid group and pure braid group, respectively. A group is right-angled Artin if it admi…

Let $\mathsf{\Gamma}$ be a graph, let $i$ be a homological degree, and let $\lambda$ be a partition. Write $\mathcal{H}_i(\mathsf{\Gamma})$ for the relevant representation-valued h…

Let $\mathcal{G}$ be a collection of graphs. Say that $\mathcal{G}$ is a set of universal generators in degree $i$ if, for every graph $\mathsf{\Gamma}$, the group…

Let $\mathsf{\Gamma}$ be a graph and let $k\geq 0$. Write $F_k(\mathsf{\Gamma})$ for its $k$-point configuration space. Folklore torsion-freeness conjecture. The space…

For a graph $G$, let $F_n(G)$ be the configuration space of $n$ ordered points in $G$, and let $cmathcal{TGI}$ be the category of topological graph embeddings. The assignment…

Let $F_n(G)$ be the configuration space of $n$ ordered points in a graph $G$. For a class of graphs, universal finite generation in degree $i$ and with $n$ particles means that a f…

Finite generation of LCS quotients. Every successive quotient of the lower central series,

Let $\Gamma$ be a planar graph, let $B_n\Gamma$ be its braid group, and let $P_3\Gamma$ be its pure braid group on three points. A group is simple-commutator-related if it has a pr…

Planar graph braid group commutator presentation conjecture. There exists a presentation for $B_2\Gamma$ such that the relators are all commutators corresponding to pairs of disjoi…