Seminario de Álgebra y Combinatoriab

Fecha: El martes 7 de junio a las 11:30

Lugar: UAM, el departamento de matemáticas, el áula 420

Speaker: Steffen Kionke

Title: The homology growth of arithmetic hyperbolic 3-manifolds in congruence towers

Astract:


A closed hyperbolic 3-manifold is the quotient manifold obtained from the action of a cocompact discrete subgroup G of SL(2,C) on the hyperbolic 3-space. A sequence of hyperbolic 3-manifolds is called a tower if the fundamental groups form a decreasing sequence. It is a challenging problem to understand the asymptotic behaviour of the Betti numbers in a given tower.

We will give a short introduction to the topic and discuss the problem for certain arithmetically defined hyperbolic 3-manifolds. We will explain how Lefschetz numbers and the representation theory of p-adic analytic groups can be used to prove asymptotic lower bounds for the Betti numbers.