JournalscmhVol. 95, No. 3pp. 515–534

Hyperbolic surfaces with sublinearly many systoles that fill

  • Maxime Fortier Bourque

    University of Glasgow, UK
Hyperbolic surfaces with sublinearly many systoles that fill cover
Download PDF

A subscription is required to access this article.

Abstract

For any ε>0\varepsilon > 0, we construct a closed hyperbolic surface of genus g=g(ε)g=g(\varepsilon) with a set of at most εg\varepsilon 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 εg\varepsilon g for the systole function, disproving the lower bound of 2g12g-1 posited by Schmutz Schaller.

Cite this article

Maxime Fortier Bourque, Hyperbolic surfaces with sublinearly many systoles that fill. Comment. Math. Helv. 95 (2020), no. 3, pp. 515–534

DOI 10.4171/CMH/495