8 problems

For even $n$, Morita constructed cycles in $H_{2n-4}(\operatorname{Out}(F_n);\mathbb{Q})$ and Conant--Vogtmann lifted them to $H_{2n-4}(\operatorname{Aut}(F_n);\mathbb{Q})$. Morita…

Let $F_n$ be the free group of rank $n\geq 2$, let $\operatorname{Out}(F_n)$ be its outer automorphism group, and let $H^*(-;\mathbb{Q})$ denote rational group cohomology. Parity s…

Let $F_n$ be the free group of rank $n\geq 2$, let $\operatorname{Aut}(F_n)$ be its automorphism group, and let $H^*(-;\mathbb{Q})$ denote rational group cohomology. Parity stabili…

Let $\mathcal{I}_{n,1}$ be the Torelli group of a genus-$n$ surface with one boundary component and let $\operatorname{IA}_n$ be the IA-automorphism group of the free group of rank…

Let $\mathcal{I}_{n,1}$ be the Torelli group of a genus-$n$ surface with one boundary component and let $\operatorname{IA}_n$ be the IA-automorphism group of the free group $F_n$.…

Let $\operatorname{IA}_n$ be the IA-automorphism group of the free group $F_n$, with its natural $\operatorname{GL}_n\mathbb{Z}$ action on rational cohomology. Vanishing conjecture…

Let $\operatorname{IA}_n$ be the IA-automorphism group of the free group $F_n$, and let $\operatorname{gr}(\operatorname{IA}_n)^i$ denote the $i$th graded piece of the graded Lie a…

Let $F_n$ be the free group of rank $n$, let $\operatorname{IA}_n$ be the kernel of $\operatorname{Aut}(F_n)\to\operatorname{GL}_n\mathbb{Z}$, and let $V^{\mathrm{fd}}$ denote the…