4 problems

The p-cell eigenmap conjecture. For every $p$-cell $\lambda$, there exists a chain map

Categorical p-half-twist conjecture. For any $w$ in the $p$-cell $\lambda$,

Categorical half-twist conjecture. If $w$ lies in the cell $\lambda$, then

Let $({\mathcal{W}},{\mathcal{S}})$ be a Coxeter system with length function $\ell$, let $A\in\mathscr{B}(\Phi^+)$, and let $w_A$ be the associated Mikado braid. Set $\beta:=w_A$,…