7 problems

Let $M_1$ and $M_2$ be manifolds with torus boundary, and let $\phi:\partial M_1\to\partial M_2$ be an orientation-reversing gluing map. Let $\mathit{HF}^{-}(M_i)$ denote the decor…

Let $K\subset Y$ be a knot with complement $M=Y\setminus\nu(K)$. Let $\mathit{HF}^{-}(Y,K)$ denote the decorated curves constructed from minus knot Floer homology in the marked tor…

Let $K\subset Y$ be a knot with complement $M=Y\setminus\nu(K)$. The decorated curves $\widehat{\mathit{HF}}(Y,K)$ are curves in the punctured torus $T_M^*$, and…

A finitely generated mixed complex is a mixed complex of the form used in the paper with finite generation understood in the source, and a bordered-mixed complex is a tuple…

Let $Y$ be a closed, oriented $3$-manifold and let $K$ be a framed knot in $Y$. Let $\mathcal H$ be a nice bordered Heegaard diagram for the infinity-framed complement…

Let $Y$ be a bordered $3$-manifold with bordered Heegaard diagram $\mathcal{H}$. The involutive type $D$ structure $\widehat{\mathit{CFDI}}(\mathcal{H})$ and involutive $A_\infty$-…

Let $\mathcal{Z}$ be an arc diagram and let $i$ be an integer. Pi-formality conjecture. The algebra $\mathcal{A}(\mathcal{Z},i)$ is $\pi$-formal, in the sense of Definition. This a…