Embedding 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  one could embed a group of type Fn into an 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 explain how one can show that the labelled Thompson groups are always acyclic. This also allows us to build acyclic groups of type Fn but not Fn+1 for any n. If time permitted, 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.