19 problems

Let $G$ be a symmetry group, let $d$ be the spatial dimension, and let $\mathrm{Witt}(G\text{-TQFT}_d)$ be the Witt group of $d$-dimensional $G$-TQFTs. Let…

Period $3p$ conjecture. $Z_p(RT)$ is a periodic map with period $3p$, for all $p$.

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 $G$ be a symmetry group. The Witt group of $G$-TQFTs is obtained from symmetry-enriched topological orders modulo the relation identifying phases that admit gapped symmetric in…

Haioun's boundary-condition conjecture. Such a boundary condition on the invertible TQFT associated with $\mathcal{C}$ should recover the non-semisimple $(2+1)$-TQFT constructed in…

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…

Generating-axioms conjecture. The full set of axioms can be derived from the following axioms, in addition to the pentagon and hexagon equations of the UMTC or braided fusion categ…

Let $\Sigma_g$ be a closed surface of genus $g$, let $\mathcal{H}_{(2g,2g)}$ denote the Hilbert space appearing in the corresponding $(2g,2g)$ theory, and let…

Let $T^2$ be the torus, let $\mathcal{H}_{(2,2)}$ denote the Hilbert space appearing in the $(2,2)$ theory, and let $\mathbb{C}[\mathbb{Z}^2\times\mathbb{Z}^2]$ be the group-algebr…

Galois-conjugacy conjecture. $\textrm{TFT}_\pm[{\cal T}_{\rm rank\;0}]$ is a Galois conjugate of $\textrm{RW}_\pm[{\cal T}_{\rm rank\;0}]$.

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 $d$ be an even dimension, let $B$ be a ball contained in the ambient space, and consider ground state wavefunctions of the generalized double semion theory (GDS), the generaliz…

Let $d$ be an even dimension and let the ambient space be any non-empty choice of ambient space. Denote the generalized double semion theory by GDS, the generalized toric code by G…

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

Let a unitary Atiyah–Segal-type $(3+1)$-TQFT be a unitary topological quantum field theory of the Atiyah–Segal type in three spatial dimensions, with partition function assigned to…