14 problems

Let $j\geq1$ and set $n=j+2$. Then $\pi_0\operatorname{Emb}(D^j,D^n)$ is the set of isotopy classes of codimension-two disk embeddings, and the invariant … has the indicated target…

Generator conjecture. The family $G(0,0,0)$ should generate

Let $j\geq1$ and $n\geq j+2$. The invariant … assigns values in the indicated target. Surjectivity conjecture for $\mu$. The invariant $\mu$ is an epimorphism for all $n\geq j+2$ w…

Let $D^j$ and $D^n$ be disks with $n>j+2$, and let the Arone–Turchin class be the generator of the copy of ${\mathbb Q}$ in … Here $\operatorname{Emb}(D^j,D^n)$ denotes the space o…

Let $n-m\geq 3$. Write $\mathrm{V}^{pl}_{n,m}=\mathrm{PL}_n/\mathrm{PL}_{n,m}$ for the PL Stiefel space, and let $\mathrm{Operad}^h(E_m,E_n)$ be the derived mapping space of the li…

Whitney invariant and Haefliger action conjecture. The coefficient $\lambda$ corresponds to the Whitney invariant $W$, while the coefficient $\mu$ corresponds to the action of

Boëchat–Haefliger invariant conjecture. The Maurer–Cartan element is related to the Boëchat–Haefliger invariant $BH$.

Lower-range hairy graph complex conjecture. The same conclusion should hold whenever

Budney–Gabai conjecture. There is an element of $\pi_0\operatorname{Diff}(D^3\times S^1,\partial)/i_*\pi_0\operatorname{Diff}(D^4,\partial)$ that is not in the image from…

Let $k>2$ and consider the spaces and Swiss Cheese operad action for $k$-stranded string links analogous to those for string $2$-links. The relevant adaptations of Theorems and are…

Let $\operatorname{Emb}(S^1,S^1\times S^3;S^1_0)$ be the based embedding space, and let $\operatorname{Diff}(S^1\times B^3\operatorname{fix}\partial)$ and…

Let $\mathrm{Emb}(S^3,\mathbb R^4)_0$ be the component of the embedding space $\mathrm{Emb}(S^3,\mathbb R^4)$ containing the standard inclusion, and let…

Let the space of light bulbs be the space of properly embedded discs in $S^2\times D^2$ that agree with $x_0\times D^2$ near their boundary, with the appropriate topology. Non-simp…

For each dimension $n$, let $\mathcal{M}_n^{\operatorname{2-conv}}$ denote the subspace of the moduli space of embedded $n$-spheres in $\mathbb{R}^{n+1}$ consisting of $2$-convex e…