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On the Homology Length Spectrum of Surfaces

Massart, Daniel ; Parlier, Hugo

In: International Mathematics Research Notices, 2017, vol. 2017, no. 8, p. 2367-2401

The homology systole of hyperbolic Riemann surfaces

Parlier, Hugo

In: Geometriae Dedicata, 2012, vol. 157, no. 1, p. 331-338

Minimal length of two intersecting simple closed geodesics

Gauglhofer, Thomas ; Parlier, Hugo

In: manuscripta mathematica, 2007, vol. 122, no. 3, p. 321-339

Fixed point free involutions on Riemann surfaces

Parlier, Hugo

In: Israel Journal of Mathematics, 2008, vol. 166, no. 1, p. 297-311

Pants Decompositions of Random Surfaces

Guth, Larry ; Parlier, Hugo ; Young, Robert

In: Geometric and Functional Analysis, 2011, vol. 21, no. 5, p. 1069-1090

Arc and curve graphs for infinite-type surfaces

Aramayona, Javier ; Fossas, Ariadna ; Parlier, Hugo

In: Proceedings of the American Mathematical Society, 2017, vol. 145, no. 11, p. 4995–5006

We study arc graphs and curve graphs for surfaces of infinite topological type. First, we define an arc graph relative to a finite number of (isolated) punctures and prove that it is a connected, uniformly hyperbolic graph of infinite diameter; this extends a recent result of J. Bavard to a large class of punctured surfaces.

On the homology length spectrum of surfaces

Massart, Daniel ; Parlier, Hugo

In: International Mathematics Research Notices, 2017, vol. 2017, no. 8, p. 2367–2401

On a surface with a Finsler metric, we investigate the asymptotic growth of the number of closed geodesics of length less than L which minimize length among all geodesic multicurves in the same homology class. An important class of surfaces which are of interest to us are hyperbolic surfaces.

Systoles and kissing numbers of finite area hyperbolic surfaces

Fanoni, Federica ; Parlier, Hugo

In: Algebraic & Geometric Topology, 2016, vol. 15, no. 6, p. 3409–3433

We study the number and the length of systoles on complete finite area orientable hyperbolic surfaces. In particular, we prove upper bounds on the number of systoles that a surface can have (the so-called kissing number for hyperbolic surfaces). Our main result is a bound which only depends on the topology of the surface and which grows subquadratically in the genus.

Curve graphs on surfaces of infinite type

Fossas, Ariadna ; Parlier, Hugo

In: Annales Academiae Scientiarum Fennicae Mathematica, 2015, vol. 40, p. 793–801

We define and study analogs of curve graphs for infinite type surfaces. Our definitions use the geometry of a fixed surface and vertices of our graphs are infinite multicurves which are bounded in both a geometric and a topological sense. We show that the graphs we construct are generally connected, infinite diameter and infinite rank.

Connecting p-gonal loci in the compactification of moduli space

Costa, Antonio F. ; Izquierdo, Milagros ; Parlier, Hugo

In: Revista Matemática Complutense, 2015, p. 1–18