6 papers
Counting and entropy for hyperbolic surface amalgams
Hugo Parlier, Yandi Wu
This paper is about closed hyperbolic surface amalgams with a focus on the growth of the number of closed geodesics. As in the case of surfaces, we show that topological and volume…
The crossing number of polynomial curve systems
Sebastian Baader, Jasmin Jörg, Hugo Parlier
We determine the crossing number of polynomial size curve systems on standard surfaces, in terms of the genus, up to high precision.
Near ideal decompositions of ideal polygons
Hugo Parlier
This article gives a short proof that all ideal polygons admit a short orthogeodesic decomposition. Specifically, all -gons admit an orthogeodesic decomposition with orthogeodes…
Graded Bridgeman dilogarithm identities on hyperbolic surfaces
Ara Basmajian, Nhat Minh Doan, Hugo Parlier +1
We establish graded versions of Bridgeman's dilogarithm identity for hyperbolic cone surfaces, including surfaces with only cusps and cone points, and provide applications to the s…
Modular systoles are extremal for the crossing number
Claire Burrin, Hugo Parlier
We study crossing numbers for systoles of congruence surfaces. Taken as a family of curves on a family of surfaces, we show that the growth rate of their intersection is optimally…
Flip-graphs of non-orientable filling surfaces
Pallavi Panda, Hugo Parlier, Lionel Pournin
Consider a surface with punctures that serve as marked points and at least one marked point on each boundary component. We build a filling surface by singling out one o…