8 problems

AMU conjecture. For a mapping class $\phi\in\Gamma$, $\phi$ is Pseudo-Anosov or reducible with Pseudo-Anosov pieces if and only if $\rho_k(\phi)$ is infinite order for large enough…

Gilmer's cut-number conjecture. For every closed, connected $3$-manifold $M$,

Let $L$ be a link with a well-defined GM series … and let $Q$ be its linking matrix with zero diagonal. General link wavefunction conjecture. The wavefunction in…

Let $K_1$ and $K_2$ be knots with well-defined GM series, and let … be the manifold obtained by gluing with $\gamma=\begin{pmatrix}r&a\p&b\end{pmatrix}$. Write the GM series as…

Let $F_{g,p}$ be the surface of genus $g$ with $p\geq 1$ boundary components, viewed with all boundary components as punctures labeled by $V(0,0)_{\overline{0}}$. Let…

Let $Z$ be the partition function of a unitary $(3+1)$-dimensional topological quantum field theory. Homotopy-invariance conjecture. The partition function of any unitary $(3+1)$-T…

Juhász–Zemke conjecture. The maps $\widehat{F}_{W,\mathcal{F}}$ coincide with the maps $F_{W,\mathcal{F}}$ defined by Juhász using sutured Floer homology.

Let $\operatorname{Cat}$ be the category of categories, let $(\infty,n)\operatorname{Cat}$ denote an $(\infty,n)$-category of higher categories, and let…