Hyperbolic surfaces with sublinearly many systoles that fill

2019/04/03 by Maxime Fortier Bourque, Bourque, Maxime Fortier · 1 citation
Engineering · Mathematics · #Advanced Numerical Analysis Techniques #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1904.01945

openalex publication_date 2019/04/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For any ε>0, we construct a closed hyperbolic surface of genus g=g(ε) with a set of at most ε g systoles that fill, meaning that each component of the complement of their union is contractible. This surface is also a critical point of index at most ε g for the systole function, disproving the lower bound of 2g-1 posited by Schmutz Schaller.

Cited by

• Thurston spine in a Teichmüller curve

Related

• Small genus, small index critical points of the systole function
• Small Systle Sets and Coxeter Groups
• The homology systole of hyperbolic Riemann surfaces
• Hyperbolic surfaces with long systoles that form a pants decomposition
• Local maxima of the systole function