Explore the intricate connections between algebra, topology, and the Grothendieck-Teichmüller group in this 51-minute lecture by D. Peterson from Stockholm. Delve into the fascinating world of top weight cohomology of M_{g,n} and its relationship to the handlebody group, gaining valuable insights into advanced mathematical concepts. Presented as part of the NCCR SwissMAP series, this talk offers a deep dive into complex mathematical structures and their interplay.