Skip to main content

Hereditarily just-infinite groups with positive first $L^2$-Betti number

Posted in
Speaker: 
Steffen Kionke
Affiliation: 
FernUniversität in Hagen
Date: 
Fri, 17/05/2024 - 10:00 - 11:00
Location: 
MPIM Lecture Hall

Examples of hereditarily just-infinite, residually finite groups are rare. Even in the well-studied class of finitely generated, residually finite infinite torsion groups, it is difficult to find examples. In this talk, we present a new construction of infinite torsion groups, which enables us to control finite quotients and normal subgroups. As an application, we describe the first examples of residually finite, hereditarily just-infinite groups with positive first $L^2$-Betti number. We will explain how the lower bound for the first $L^2$-Betti number is obtained and we will indicate why these groups have polynomial normal subgroup growth (answering a question of Barnea and Schlage-Puchta). Eventually, we give an outlook to related constructions.

This is based on joint work with Eduard Schesler.

© MPI f. Mathematik, Bonn Impressum & Datenschutz
-A A +A