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dc.contributor.advisorGadgil, Siddhartha
dc.contributor.authorSanki, Bidyut
dc.date.accessioned2018-01-31T05:17:04Z
dc.date.accessioned2018-07-31T06:09:12Z
dc.date.available2018-01-31T05:17:04Z
dc.date.available2018-07-31T06:09:12Z
dc.date.issued2018-01-31
dc.date.submitted2014
dc.identifier.urihttps://etd.iisc.ac.in/handle/2005/3049
dc.identifier.abstracthttp://etd.iisc.ac.in/static/etd/abstracts/3913/G26900-Abs.pdfen_US
dc.description.abstractGiven a hyperbolic surface, the set of all closed geodesics whose length is minimal form a graph on the surface, in fact a so called fat graph, which we call the systolic graph. The central question that we study in this thesis is: which fat graphs are systolic graphs for some surface -we call such graphs admissible. This is motivated in part by the observation that we can naturally decompose the moduli space of hyperbolic surfaces based on the associated systolic graphs. A systolic graph has a metric on it, so that all cycles on the graph that correspond to geodesics are of the same length and all other cycles have length greater than these. This can be formulated as a simple condition in terms of equations and inequations for sums of lengths of edges. We call this combinatorial admissibility. Our first main result is that admissibility is equivalent to combinatorial admissibility. This is proved using properties of negative curvature, specifically that polygonal curves with long enough sides, in terms of a lower bound on the angles, are close to geodesics. Using the above result, it is easy to see that a subgraph of an admissible graph is admissible. Hence it suffices to characterize minimal non-admissible fat graphs. Another major result of this thesis is that there are infinitely many minimal non-admissible fat graphs (in contrast, for instance, to the classical result that there are only two minimal non-planar graphs).en_US
dc.language.isoen_USen_US
dc.relation.ispartofseriesG26900en_US
dc.subjectHyperbolic Surfacesen_US
dc.subjectSystolic Graphsen_US
dc.subjectFat Graphsen_US
dc.subjectGeodesicsen_US
dc.subjectHyperbolic Geometryen_US
dc.subjectGraphic Methodsen_US
dc.subjectPolygonal Quasi-Geodesicsen_US
dc.subjectQuasi-geodesicsen_US
dc.subjectGauss-Bonnet Theoremen_US
dc.subjectHyperbolic Trigonometryen_US
dc.subjectGraphsen_US
dc.subjectTrivalent Graphsen_US
dc.subject.classificationMathematicsen_US
dc.titleShortest Length Geodesics on Closed Hyperbolic Surfacesen_US
dc.typeThesisen_US
dc.degree.namePhDen_US
dc.degree.levelDoctoralen_US
dc.degree.disciplineFaculty of Scienceen_US


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