Cutting and pasting in the Torelli subgroup of Out(Fn)

Landgraf, Jacob

doi:10.2140/agt.2025.25.1

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Cutting and pasting in the Torelli subgroup of $\operatorname{Out}(F_{n})$

Jacob Landgraf

Algebraic & Geometric Topology 25 (2025) 1–38

DOI: 10.2140/agt.2025.25.1

Abstract

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.

Keywords

automorphism groups of free groups, mapping class groups, Torelli group, $3$-manifolds, Birman exact sequence, finite generation

Mathematical Subject Classification

Primary: 57K20, 57K30, 57M07

References

Publication

Received: 18 November 2021

Revised: 15 September 2023

Accepted: 30 September 2023

Published: 5 March 2025

Authors

Jacob Landgraf
Department of Mathematics University of Notre Dame Notre Dame, IN United States

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Volume 25, issue 1 (2025)