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 | |
|---|---|
| Format | Journal Article |
| Language | English |
| Published |
03.04.2019
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| Subjects | |
| Online Access | Get full text |
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| Abstract | 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. |
|---|---|
| AbstractList | 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. |
| Author | Bourque, Maxime Fortier |
| Author_xml | – sequence: 1 givenname: Maxime Fortier surname: Bourque fullname: Bourque, Maxime Fortier |
| BackLink | https://doi.org/10.48550/arXiv.1904.01945$$DView paper in arXiv |
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| Snippet | 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... |
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| SubjectTerms | Mathematics - Geometric Topology |
| Title | Hyperbolic surfaces with sublinearly many systoles that fill |
| URI | https://arxiv.org/abs/1904.01945 |
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