Counting commensurability classes of hyperbolic manifolds (RTG Day)
 Date:22.11.2016
 Speaker:Arie Levit

Time:13:30 h

Abstract: Counting questions are an interesting direction in the study of hyperbolic manifolds. By a classical result of Wang, in dimension > 3 there are only finitely many hyperbolic manifolds up to any finite volume V. More recently, Burger, Gelander, Lubotzky and Mozes showed that this number grows like V^V.
In this talk we focus on the number of commensurability classes of hyperbolic manifolds. Two manifolds are commensurable if they admit a common finite cover. We show that in dimension > 3 this number grows like V^V as well.
Since the number of arithmetic commensurability classes grows ~ polynomially, our result implies that nonarithmetic manifolds account for “most" commensurability classes. Another application has to do with quasiisometry classes of lattices.
We will explain the ideas involved in the proof, which include a mixture of arithmetic, hyperbolic geometry and some combinatorics.
This is a joint work with Tsachik Gelander.

Place:1.067 (20.30)