Hyperbolic geometry and manifolds: Volume

Geodesics on hyperbolic surfaces and volumes of link complements in Seifert-fibered spaces- José Andrés Rodriguez Migueles (University of Helsinki)

Abstract: Let Γ be a link in a Seifert-fibered space M over a hyperbolic surface Σ that projects injectively to a collection of closed geodesics γ in Σ. When γ is filling, the complement of Γ in M admits a hyperbolic structure of finite volume. We give bounds of its volume in terms of topological invariants of (γ,Σ).

Uniform models for random 3-manifolds- Gabriele Viaggi (University of Heidelberg)

Abstract: As discovered by Thurston, hyperbolic 3-manifolds are abundant among all 3-manifolds. In many examples, the generic element in a family of 3-manifolds sharing a common combinatorial description admits such a hyperbolic structure. The family of random 3-manifolds (Dunfield and Thurston model) is one of these examples. The existence of a hyperbolic metric on such random objects has been established by Maher, exploiting the solution of the Geometrization conjecture by Perelman. In this talk, I will describe a more constructive approach to this result and give an explicit construction for the metric that only uses tools from the deformation theory of Kleinian groups. The metric obtained is explicit enough to allow the computation of geometric invariants such as volume and diameter. Joint with Peter Feller and Alessandro Sisto.

Hyperbolic Limits of Cantor sets complements in the Sphere- Franco Vargas Pallete (Yale University)

Abstract: In this talk we will show that if M is a hyperbolic manifold that embeds in $S^3$ with no $Z^2$ in $pi_1$, then M can be approximated (in the geometric sense) by hyperbolic metrics on Cantor set complements in $S^3$. This is joint work with Tommaso Cremaschi.

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