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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Main Author | |
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Format | Journal Article |
Language | English |
Published |
03.04.2019
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Subjects | |
Online Access | Get full text |
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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. |
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DOI: | 10.48550/arxiv.1904.01945 |