A Birman exact sequence for the Torelli subgroup of Aut(F_n)

TL;DR

This paper constructs an analogue of the Birman exact sequence specifically for the Torelli subgroup of automorphisms of free groups, advancing understanding of its algebraic structure and homology.

Contribution

It introduces a new exact sequence for the Torelli subgroup of Aut(F_n), extending previous work on the entire automorphism group.

Findings

Established a Birman exact sequence for the Torelli subgroup

Provided tools for studying the second homology of the Torelli group

Enhanced algebraic understanding of Torelli subgroup structure

Abstract

We develop an analogue of the Birman exact sequence for the Torelli subgroup of Aut(F_n). This builds on earlier work of the authors who studied an analogue of the Birman exact sequence for the entire group Aut(F_n). These results play an important role in the authors' recent work on the second homology group of the Torelli group.