Hyperbolic surfaces with sublinearly many systoles that fill

For any $\varepsilon>0$, we construct a closed hyperbolic surface of genus $g=g(\varepsilon)$ with a set of at most $\varepsilon g$ 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 $\varepsilon...

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Bibliographic Details
Main Author Bourque, Maxime Fortier
Format Journal Article
LanguageEnglish
Published 03.04.2019
Subjects
Mathematics - Geometric Topology
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Summary:For any $\varepsilon>0$, we construct a closed hyperbolic surface of genus $g=g(\varepsilon)$ with a set of at most $\varepsilon g$ 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 $\varepsilon g$ for the systole function, disproving the lower bound of $2g-1$ posited by Schmutz Schaller.
DOI:10.48550/arxiv.1904.01945