Cutting and Pasting in the Torelli subgroup of Out($F_n$)

Jacob Landgraf

Published 2021-06-27Version 1

Using ideas from 3-manifolds, Hatcher--Wahl defined a notion of automorphism groups of free groups with boundary. We study their Torelli subgroups, adapting ideas introduced by Putman for surface mapping class groups. Our main results show that these groups are finitely generated, and also that they satisfy an appropriate version of the Birman exact sequence.