Embed groups into acyclic groups

  • Venue:

    Bldg. 20.30, SR 3.069

  • Date:

    29.07.2025

  • Speaker:

    Xiaolei Wu

  • Time:

    15:15 Uhr

  • We first discuss various embedding results for groups in the literature. Then we talk about how could one embed a group of type Fn into a acyclic group of type Fn. The embedding we have uses the labelled Thompson group which goes back to Thompson's Splinter group in the 1980s. We exlain how one can show that the labeled Thompson group is always acyclic. This also allows us to build acyclic groups of type Fn but not Fn+1 for any n. If time permited, I will also discuss related results in the simple setting using the twisted Brin–Thompson groups. This is based on a joint work in progress with Martin Palmer.