8 problems

For each natural number $m$, let $T_{2m}$ be the full projective tilting module in the relevant parabolic category ${\mathcal O}$ for $\mathfrak{sl}_{2m}$, and let ${\mathcal H}_m$…

The paper considers functorial invariants of oriented tangles and cobordisms, obtained by assigning functors to tangle diagrams and natural transformations to cobordisms. These inv…

A $1$-$1$ tangle invariant is an invariant assigned to a tangle with one incoming and one outgoing endpoint; reversing a knot reverses its orientation. Conjecture. The $1$-$1$ tang…

The tangle invariants constructed by Naisse and Putyra, Vaz, and Schelstraete–Vaz are defined as lifts of odd Khovanov homology to tangles. Naisse–Putyra's conjecture. Naisse and P…

Let $T$ be a pointed 2-tangle and let $P^*\cong\partial(D^3,T)$ be the pillowcase. Write $I(T)$, $I^\natural(T)$ and $I^\sharp(T)$ for the proposed instanton-theoretic immersed cur…

Let $T$ be a 2-tangle, let $R_\pi(T)\looparrowright P^*$ be its holonomy-perturbed traceless character variety, and let $b\in \mathit{CF}(R_\pi(T),R_\pi(T))$. Let…

The paper constructs a graded 2-functor from an odd version of a level 2 cyclotomic half 2-Kac--Moody algebra associated to $\mathfrak{gl}_n$ to the bicategory of quasi-associative…

Let $(Y_2,L_2)$ be an $n$-tangle in a decomposition of a link along a sphere, with $(Y_1,L_1)$ chosen to be an unknotted, trivial tangle, and let…