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

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.

arXiv comment41 pages, 15 figures; added Theorem E giving the abelianizations of these Torelli groups

References in corpus (13)

• Stabilization for mapping class groups of 3-manifolds
• Dimension of the Torelli group for Out(F_n)
• Cutting and Pasting in the Torelli Group
• Stabilization for the automorphisms of free groups with boundaries
• Integrality in the Steinberg module and the top-dimensional cohomology of SL_n(O_K)
• The complex of partial bases for F_n and finite generation of the Torelli subgroup of Aut(F_n)
• Automorphisms of free groups with boundaries
• A Birman exact sequence for Aut(F_n)
• Obtaining presentations from group actions without making choices
• The mapping class group of connect sums of $S^2\times S^1$
• The commutator subgroups of free groups and surface groups
• The Birman exact sequence for 3-manifolds
• A Birman exact sequence for the Torelli subgroup of Aut(F_n)