3 problems

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 $G\le \operatorname{\mathsf{PL}}([0,1])$ 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…