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Systoles in translation surfaces (1707.05060v3)
Published 17 Jul 2017 in math.MG and math.GT
Abstract: For a translation surface, we define the systole to be the length of the shortest saddle connection. We give a characterization of the maxima of the systole function on a stratum, and give a family of examples providing local but nonglobal maxima on each stratum of genus at least three. We further study the relation between (locally) maximal values of the systole function and the number of shortest saddle connections.
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