20 citations · 169 across the 52 of their papers we have counts for
5 papers · 2 filters
Smoothing curves carefully
Hugo Parlier
This paper proves an elementary topological fact about closed curves on surfaces, namely that by carefully smoothing an intersection point, one can reduce self-intersection by exac…
A topological viewpoint on curves via intersection
Hugo Parlier, Binbin Xu
This paper explores the relationship between closed curves on surfaces and their intersections. Like Dehn-Thurston coordinates for simple curves, we explore how to determine closed…
Counting geodesics between surface triangulations
Hugo Parlier, Lionel Pournin
Given a surface equipped with a set of marked points, we consider the triangulations of with vertex set . The flip-graph of whose vertices are these triangulatio…
A shorter note on shorter pants
Hugo Parlier
This note is about variations on a theorem of Bers about short pants decompositions of surfaces. It contains a version for surfaces with boundary but also a slight improvement on t…
Universal families of arcs and curves on surfaces
Niloufar Fuladi, Arnaud de Mesmay, Hugo Parlier
The main goal of this paper is to investigate the minimal size of families of curves on surfaces with the following property: a family of simple closed curves on a surface real…