CUSO Graduate Colloquium 2024

Talk

Perturbed bouquets and their realisability by systoles

Jasmin Jörg

on  We, 14:30 ! Livein  B78for  45min

Given a closed hyperbolic surface, one may consider the collection of all systoles, that is, all geodesics of minimal length. Systoles necessarily form a 1-system, a system of simple closed curves intersecting pairwise at most once. On the other hand, it is not clear what 1-systems can be realised by systoles. We consider the subclass of 1-systems obtained by perturbing a bouquet, present some obstructions to them being systolic and indicate why most of them fail to be systoles for any Riemannian metric.

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