20 citations · 169 across the 52 of their papers we have counts for
4 papers · 2 filters
The shortest non-simple closed geodesics on hyperbolic surfaces
Ara Basmajian, Hugo Parlier, Hanh Vo
This article explores closed geodesics on hyperbolic surfaces. We show that, for sufficiently large , the shortest closed geodesics with at least self-intersections, taken a…
Quadratis Puzzles
Mario Gutiérrez, Hugo Parlier, Paul Turner
We introduce a family of reconfiguration puzzles arising from ideas in geometry and topology. We present their construction from square-tiled shapes, discuss some of the underlying…
Quasisymmetric maps, shears, lambda lengths and flips
Hugo Parlier, Dragomir Šarić
We study quasisymmetric maps, which act on the boundary of the hyperbolic plane, by looking at their action on the Farey triangulation. Our main results identify exactly which quas…
The coarse geometry of hexagon decomposition graphs
Funda Gültepe, Hugo Parlier
We define and study graphs associated to hexagon decompositions of surfaces by curves and arcs. One of the variants is shown to be quasi-isometric to the pants graph, whereas the o…