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Systoles in translation surfaces

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 23 Aug 2021Embargo end date: 01 Jan 2017 France Publisher:Societe Mathematique de FranceJournal:Bulletin de la Société mathématique de France (issn: 0037-9484, eissn: 2102-622X,

Authors: Boissy, Corentin; Geninska, Slavyana;

doi: 10.24033/bsmf.2833 , 10.48550/arxiv.1707.05060

arXiv: http://arxiv.org/abs/1707.05060

Systoles in translation surfaces

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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.

21 pages, 7 figures. Minor corrections

Country

France

Related Organizations

University of Toulouse II - Le Mirail
France
INSA de Toulouse
France
University of Toulouse
France

Keywords

MSC (2010) Primary 32G15, systoles, 610, Metric Geometry (math.MG), Geometric Topology (math.GT), 510, Mathematics - Geometric Topology, Secondary 30F30, Mathematics - Metric Geometry, [MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT], translation surfaces, FOS: Mathematics, moduli spaces, [MATH.MATH-MG] Mathematics [math]/Metric Geometry [math.MG], [MATH.MATH-MG]Mathematics [math]/Metric Geometry [math.MG], [MATH.MATH-GT] Mathematics [math]/Geometric Topology [math.GT]

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