5 problems

Let \bar\mathcal B_g be the subgroup of $\mathcal M_{g,1}$ consisting of diffeomorphisms of the surface $\Sigma_g$ that extend over the handlebody $\bar T_g$. Let…

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…

Let $H$ be the standard symplectic representation in genus $2$, let $V_\boxplus$ be the weight $-2$ ${\mathrm{Sp}}(H)$-module in the minimal presentation … and, after decomposing a…

Let $F_n$ be the free group of rank $n$, let $\mathcal{L}_n$ be the free Lie algebra associated with the lower central series of $F_n$, and let $\mathrm{Der}^+(\mathcal{L}_n)$ be t…