4 problems

Injectivity and order-preserving image conjecture. This homomorphism is injective, and its image consists precisely of the order-preserving automorphisms.

Let $F$ be Thompson's group, and let $H$ be a finitely generated subgroup of $F$. A finite generating set of a subgroup of $\operatorname{Homeo}_+(I)$ is geometrically fast if it h…

For $k\geq 1$, let $\mathrm{Spec}^{\mathrm{max}}_k(F)$ denote the collection of isomorphism classes of $k$-generated subgroups of Thompson's group $F$ that are visible under the ma…

Let $r_n$ be the number of reduced pairs of binary trees with $n$ carets in each tree. Woodruff's conjecture. The number $r_n$ is proportional to … This asymptotic prediction conce…