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On the length spectrum of random hyperbolic 3-manifolds

By Anna Roig Sanchis

Appears in collection : Probability and Geometry in, on and of non-Euclidian spaces / Probabilités et géométrie dans, sur et des espaces non-euclidiens

We are interested in studying the behavior of geometric invariants of hyperbolic 3-manifolds, such as the length of their geodesics. A way to do so is by using probabilistic methods. That is, we consider a set of hyperbolic manifolds, put a probability measure on it, and ask what is the probability that a random manifold has a certain property. There are several models of random manifolds. In this talk, I will explain one of the principal probabilistic models for 3 dimensions and I will present a result concerning the length spectrum - the set of lengths of all closed geodesics - of a 3-manifold constructed under this model.

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Citation data

  • DOI 10.24350/CIRM.V.20100003
  • Cite this video Roig Sanchis Anna (10/3/23). On the length spectrum of random hyperbolic 3-manifolds. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20100003
  • URL https://dx.doi.org/10.24350/CIRM.V.20100003

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