8 problems

Bounded-class elementary amenable–$F$ alternative conjecture. Every subgroup of $PL_o(I)$ is either elementary amenable of some class $lpha$ with

Elementary amenable–$F$ alternative conjecture. Every subgroup of $PL_o(I)$ is either elementary amenable or it contains a subgroup that is isomorphic to $F$.

Fixed-point conjecture. There exists a generating set $S$ of $\Gamma$ such that every first-step primitive element with respect to $S$ fixes a point in $I$, while there exists…

Let $f\in {PL}_+S^1$ be a piecewise linear orientation-preserving circle homeomorphism that maps $\mathbb{Q}$ to $\mathbb{Q}$ and whose slopes are powers of a single rational numbe…

Let $G\le \operatorname{\mathsf{PL}}([0,1])$ be a finitely generated group of piecewise linear homeomorphisms of $[0,1]$. Its standard action is assumed to be conjugate to a…

Let $G\leq \mathrm{PL}_+ I$ be a finitely generated subgroup. An $F$-obstruction is a pair of elements of $G$ forming an $F$-obstruction in the sense of Theorem. Embedding conjectu…

Let $I$ be the interval, let $\operatorname{PL}_+(I)$ be the group of all piecewise linear elements of $\operatorname{Homeo}_+(I)$, let $H$ be a finitely generated subgroup of…

Brin group embedding conjecture. Every finitely generated non-soluble subgroup $G<PL_+(I)$ contains an embedded copy of Brin's group $B$.