6 problems

Let $A_\Gamma$ be an Artin group and let $\chi:A_\Gamma\to\mathbb{R}$ be a character. Let $\mathrm{Liv}^\chi$ denote the living subgraph associated to $\chi$, and let…

Let $A_\Gamma$ be an Artin group satisfying the $K(\pi,1)$-conjecture, and let $\chi:A_\Gamma\to\mathbb{R}$ be a character. Write $\mathrm{Liv}^\chi$ for the living subgraph, and c…

Let $A_\Gamma$ be an Artin group and let $\chi:A_\Gamma\to\mathbb{R}$ be a character. The living subgraph $\mathrm{Liv}^\chi\subset\Gamma$ is obtained by deleting vertices $v$ with…

BNSR-invariant conjecture. For any $S$ and $r$,

Conjecture I. Under this identification,

Let $m\in\mathbb{N}\cup\{\infty\}$, let $\psi$ be the character considered in the surrounding discussion, and let the ambient group be one of the Lodha--Moore groups $G$, $G_y$,…