2 problems

Assume $(p_0)_*(\mu_k)=0$, and construct a cycle $u\in Z_{4k+1}(\mathrm{GL}(2k+3,\mathbb{Z});\mathbb{Q})$ by bounding the relevant abelian cycle in $\mathrm{Out}\,F_{2k+3}$ and its…

Let $k$ be an integer with $k\geq 1$. The Borel regulator class $\beta_{2k+1}$ is a cohomology class in $H^{4k+1}(\mathrm{GL}(2k+2,\mathbb{Z});\mathbb{R})$. Critical-rank vanishing…