5 problems

Let $F_n$ be the free group of rank $n$, let $K$ be the compact group appearing in the paper, and let $\operatorname{Hom}(F_n,K)/K$ denote the quotient of the representation variet…

For each integer $i\geq1$, let … be the homology class constructed from Kontsevich's graph-homology construction. Morita's conjecture. The classes $\mu_i$ are non-trivial for all…

Let $D53D$ be a finitely generated free group, let $D52CD66D61\operatorname{Out}(D53D)$ act on the cyclic splitting complex $D9D$. An element is loxodromic if it acts loxodromicall…

Integral homology conjecture. The map $\mathcal{G}^1_n(X)\to\mathcal{G}_n(X)$ induces an isomorphism on homology in degrees $2*\leq n-3$.

Redundant-representation conjecture. (a) The action of $\operatorname{Out}(F_n)$ on $R$ is ergodic.