The systole of hyperbolic surfaces

Abstract: The systole of a Riemannian manifold is defined as the infimal length of its closed geodesics that are not contractible and was studied by Berger and Gromov in the 70's and 80's. In this talk, I will survey recent results on the systole of closed hyperbolic surfaces. In particular, I will explain how to construct a surface out of polygons glued along a graph in a way that we can determine its systole. Variants of this construction yield numerous local maxima for the systole, critical points of lower index than expected, and are used to prove that the dimension of a certain set defined by Thurston is larger than hoped.

algebraic geometryanalysis of PDEsalgebraic topologycomplex variablesdifferential geometrygeneral topologygeometric topologyK-theory and homologymetric geometrysymplectic geometry

Audience: researchers in the topic

CRM - Séminaire du CIRGET / Géométrie et Topologie

Series comments: Hybrid seminar of geometry and topology. Laboratory : CIRGET - www.cirget.uqam.ca The homepage of the seminar is www.cirget.uqam.ca/fr/seminaires.html

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