Seminario Teoría de Grupos
Torsion homology growth and L^2-torsion
Ponente: Sam Hughes (University of Bonn)Fecha: jueves 22 de mayo de 2025 - 10:00Lugar: Aula Naranja, ICMAT
Resumen:
The L^2-torsion of a hyperbolic (2n+1)-manifold is proportional to its hyperbolic volume. The invariant can (in principle) be defined for any cocompact free L^2-acyclic G-CW complex X and may be thought of as a notion of hyperbolic volume for X/G. When G is residually finite a conjecture of L\"uck relates the growth rate of the size of torsion in the homology of finite covers of X/G with the L^2-torsion of X. I will discuss this conjecture and recent results related to it in the context of automorphisms of groups. Based on joint work with Wolfgang L\"uck and older joint work with Naomi Andrew, Yassine Guerch, and Monika Kudlinska.
