20 citations · 169 across the 52 of their papers we have counts for
52 papers · 1 filter
Ordering curves on surfaces
Hugo Parlier, Hanh Vo, Binbin Xu
We study the order of lengths of closed geodesics on hyperbolic surfaces. Our first main result is that the order of lengths of curves determine a point in Teichmüller space. In an…
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…
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…
The topological types of length bounded multicurves
Hugo Parlier
This article discusses inequalities on lengths of curves on hyperbolic surfaces. In particular, a characterization is given of which topological types of curves and multicurves alw…
Bounded geometry with no bounded pants decomposition
Ara Basmajian, Hugo Parlier, Nicholas G. Vlamis
We construct a quasiconformally homogeneous hyperbolic Riemann surface-other than the hyperbolic plane-that does not admit a bounded pants decomposition. Also, given a connected or…
Ideally, all infinite type surfaces can be triangulated
Alan McLeay, Hugo Parlier
We show that any surface of infinite type admits an ideal triangulation. Furthermore, we show that a set of disjoint arcs can be completed into a triangulation if and only if, as a…
The simple separating systole for hyperbolic surfaces of large genus
Hugo Parlier, Yunhui Wu, Yuhao Xue
In this note we show that the expected value of the separating systole of a random surface of genus with respect to Weil-Petersson volume behaves like as the genus g…
Flip graphs for infinite type surfaces
Ariadna Fossas, Hugo Parlier
We associate to triangulations of infinite type surface a type of flip graph where simultaneous flips are allowed. Our main focus is on understanding exactly when two triangulation…
Systoles and diameters of hyperbolic surfaces
Florent Balacheff, Vincent Despré, Hugo Parlier
In this article we explore the relationship between the systole and the diameter of closed hyperbolic orientable surfaces. We show that they satisfy a certain inequality, which can…
Prime orthogeodesics, concave cores and families of identities on hyperbolic surfaces
Ara Basmajian, Hugo Parlier, Ser Peow Tan
We prove and explore a family of identities relating lengths of curves and orthogeodesics of hyperbolic surfaces. These identities hold over a large space of metrics including ones…
Geodesic and orthogeodesic identities on hyperbolic surfaces
Hugo Parlier
The lengths of geodesics on hyperbolic surfaces satisfy intriguing equations, known as identities, relating these lengths to geometric quantities of the surface. This paper is abou…
Measuring pants
Nhat Minh Doan, Hugo Parlier, Ser Peow Tan
We investigate the terms arising in an identity for hyperbolic surfaces proved by Luo and Tan, namely showing that they vary monotonically in terms of lengths and that they verify…
Geometric simplicial embeddings of arc-type graphs
Hugo Parlier, Ashley Weber
In this paper, we investigate a family of graphs associated to collections of arcs on surfaces. These {\it multiarc graphs} naturally interpolate between arc graphs and flip graphs…
Minimal length product over homology bases of manifolds
Florent Balacheff, Steve Karam, Hugo Parlier
Minkowski's second theorem can be stated as an inequality for -dimensional flat Finsler tori relating the volume and the minimal product of the lengths of closed geodesics which…
Quantifying the sparseness of simple geodesics on hyperbolic surfaces
Peter Buser, Hugo Parlier
The goal of the article is to provide different explicit quantifications of the non density of simple closed geodesics on hyperbolic surfaces. In particular, we show that within an…
The maximum number of systoles for genus two Riemann surfaces with abelian differentials
Chris Judge, Hugo Parlier
In this article, we provide bounds on systoles associated to a holomorphic -form on a Riemann surface . In particular, we show that if has genus two, then, up to homo…
Counting curves, and the stable length of currents
Viveka Erlandsson, Hugo Parlier, Juan Souto
Let be a curve on a surface of genus and with boundary components and let be a discrete and cocompact action on some metric space. We s…