4 problems

Conjecture. One has

Witzel's conjecture. The $\Sigma$-invariants of $\Gamma$ satisfy

Let $\Gamma$ be a finite simplicial graph with edges labeled by integers greater than one, and let $G=G_{\Gamma}$ be its Artin group. For a non-zero character…

Let $(H_n)_{n\in\mathbb{N}}$ be the Houghton groups. For $n\geq 2$, let $\chi_1,\dots,\chi_n$ be the characters defined by the eventual translation lengths, with…