1 citations · 1 across the 3 of their papers we have counts for
4 papers
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…
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,…
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…
On quotients of congruence subgroups of braid groups
Jessica Appel, Wade Bloomquist, Katie Gravel +1
The integral Burau representation provides a map from the braid group into a group of integral matrices. This allows for a definition of congruence subgroups of the braid group as…