For any , we construct a closed hyperbolic surface of genus with a set of at most 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 for the systole function, disproving the lower bound of 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. 515–534DOI 10.4171/CMH/495