| Résume | Most closed 3-manifolds support a hyperbolic metric, uniquely
determined by their topology. Extracting geometric information from a
combinatorial presentation of the manifold is an intriguing and usually
hard problem. In this talk, instead of focusing on a single 3-manifold, we
study the growth rate of geometric invariants in families of 3-manifolds
that share a common combinatorial description. Specifically, we will work
with families of random 3-manifolds as introduced by Dunfield and
Thurston. We will introduce an explicit negatively curved metric on them
and use it to compute volume and spectral gap of the underlying hyperbolic
structures. Joint work with Ursula Hamenstädt. |
