14 problems

A finitely generated group is accessible if it admits a finite graph-of-groups decomposition with finite edge groups and vertex groups having at most one end. Wall's accessibility…

Swarup's Strong Accessibility Conjecture. Decompose $G$ maximally over finite subgroups, then decompose each resulting vertex group maximally over two-ended subgroups, and repeat t…

A finitely generated group $G$ is called accessible if it splits as a finite graph of groups with finite edge groups and vertex groups with at most one end. Wall's accessibility co…

Let $r\in[2,+\infty]$, and consider $C^{r}$ partially hyperbolic diffeomorphisms, whether volume preserving or not. A diffeomorphism is stably accessible if it has the accessibilit…

Let $f$ be a $C^{2}$ partially hyperbolic, volume-preserving diffeomorphism, and suppose that $f$ has the essential accessibility property, meaning that every measurable set satura…

Let $G$ be a finitely generated group acting on a tree, and consider both Weidmann's accessibility bound for $(k,C)$-acylindrical actions on a $C$-partially reduced tree and Bestvi…

Let $G$ be a finitely generated group acting on a tree, with the action subject to the hypotheses in Weidmann's accessibility theorem and with edge stabilisers restricted as in Bes…

Let $G$ be a quasi-transitive locally finite connected graph. A process of splittings repeatedly factors any factor with more than one end, and stops when all factors have at most…

Let $M$ be a manifold and let $f:M\to M$ be a partially hyperbolic diffeomorphism. Say that $f$ is $r$-bunched when it satisfies the $r$-bunching condition. Wilkinson's conjecture.…

Let $M$ be a manifold and let $f:M\to M$ be a partially hyperbolic diffeomorphism. For $x\in M$, the accessibility class $AC(x)$ is the set of points that can be joined to $x$ by a…

Let $\mathcal{M}$ be a compact connected smooth manifold, and let $f$ be a volume-preserving partially hyperbolic diffeomorphism of $\mathcal{M}$ with stable, center, and unstable…

A locally finite graph is transitive if its automorphism group acts transitively on its vertices, and it is accessible if there exists some $k\in\mathbb{N}$ such that any two ends…

Accessibility-class regularity conjecture. Every accessibility class for $f$ is an injectively immersed, $C^r$ submanifold of $M$.

Let $\mathcal{D}$ be the diffeomorphism group of a manifold, equipped with the distribution $\mathcal T$. A path in $\mathcal{D}$ is horizontal when it is tangent to $\mathcal T$.…