8 problems

Let $M$ be a compact manifold and let $\operatorname{Diff}^r(M)$ be the space of $C^r$-diffeomorphisms, where $r\geq 1$, endowed with the $C^r$-topology. Let $\mathcal{MS}$ denote…

Boundary-determination conjecture. If $\partial X$ and $\partial X'$ are diffeomorphic, then $X$ and $X'$ are diffeomorphic.

Let $M$ be a closed manifold with a volume, let $k\ge 1$, and let $\operatorname{Diff}^k_{\operatorname{vol}}(M)$ denote the space of $C^k$ volume-preserving diffeomorphisms of $M$…

Nontriviality conjecture. The diffeomorphism $f$ is not smoothly isotopic to the identity. This would provide a potentially nontrivial pseudo-isotopy of $S^4$ arising from the disc…

Let $Y$ be a closed, connected, oriented $3$-manifold. A compact, oriented smooth $4$-manifold $W$ with boundary $\partial W=Y$ has mapping class groups of diffeomorphisms and home…

Let $X$ be a 4-manifold with $k_1 X=0$. The subgroups $\Theta(\mathcal{J}(X))$ and $\Theta(\mathcal{J}(X)\cap\ker\Sigma)$ are defined in the target of the pseudo-isotopy invariant…

Let $f$ be the diffeomorphism under consideration, and let $g_i=h_i f h_i^{-1}$ be tidy perturbations of $f$ converging to $g=hfh^{-1}$, where the diffeomorphisms $h_i$ converge to…

Let $S^1$ be the circle, let $\operatorname{Diff}^1(S^1)$ denote the space of $C^1$ diffeomorphisms of $S^1$, and for $f\in\operatorname{Diff}^1(S^1)$ let $C(f)$ be its centralizer…