5 problems

Let $g$ be sufficiently large, let $\mathcal{HI}_g^1$ denote the handlebody Torelli group, and let $B_3^{b_i}$ be the subspace defined from the Birman–Craggs–Johnson homomorphism.…

Let $F_2$ be the free group of rank $2$, let $F_2^n$ denote its $n$-fold direct product, and let $\mathcal{H}_g$ be the handlebody group of genus $g$. A subgroup or map is quasi-is…

Let $\mathcal{H}_g$ be the handlebody group, let $\mathcal{K}_g$ be the Johnson kernel of the mapping class group, and define the handlebody Johnson kernel by … A separating meridi…

Let $\mathcal{HI}_{g,p}^b$ be the handlebody Torelli group, and let $\tau(\mathcal{HI}_{g,p}^b)$ and $\sigma(\mathcal{HK}_{g,p}^b)$ denote the images of the Johnson and Birman--Cra…

Let $\mathcal{H}_B\mathcal{I}_{g,p}^b$ denote the handlebody hyperelliptic Torelli group, and let $\overline{W}_{\mathbb Q}$ and $W_{\mathbb Q}$ be the rational modules appearing i…