3 papers
math.GT2026
The Birman--Craggs--Johnson homomorphism and the handlebody Torelli group
Annie Holden
We use the Birman--Craggs--Johnson (BCJ) homomorphism to study the intersection of the handlebody group with the Torelli group and with the Johnson kernel. For genus , we d…
math.GT2026
Abelianizations of finite-index subgroups of the handlebody group
Annie Holden
For genus , it is an open question whether the mapping class group of a handlebody contains a finite-index subgroup with nontrivial rational abelianization. In this paper,…
math.GT2025
Johnson homomorphisms and the second rational cohomology of handlebody Torelli groups
Annie Holden
We introduce two Torelli subgroups of the handlebody group. The group is the subgroup of the handlebody group acting trivially on the first homology of the boundary su…