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Hyperbolic surfaces are given by pairs of pants glued with twists, with pairs of pants given by right-angled hexagons.
For each of these, we determine if there is an approximate systole with a large number of curves, where the systole is the set of geodesics of minimal length.
Goal is to try to determine, by compact enumeration, the largest systole for a surface of genus 3.
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The existence of a systole implies that of an epsilon-aprroximate systole, and hence we can get an upper bound on the size of a systole.
By compactness, this is also a lower bound for epsilon small enough, but we need this to be effective, or have an alternative argument using, for example, implicit function theorem or real algerbraic geometry.
The text was updated successfully, but these errors were encountered: