3 problems

Let $n\geq2$, and let $\depu n$ be a decorated once punctured $n$-gon. Its full arc complex is the simplicial complex whose simplices consist of collections of pairwise compatible…

Schleimer's conjecture. There is a constant $t(M)$ such that the monodromy of every fibered knot $K\subset M$ has translation distance in the arc complex of the fiber at most…

Let $S$ be a surface with a set of marked points $P$, let $C$ be a relevant boundary component, and let $\alpha,\beta\in\mathcal{A}_{C}(S,P)$ be arcs. Write…