4 problems

Let $M$ be a 3-manifold containing unstabilized Heegaard surfaces $F$ and $G$, neither of which has topological index $1$. Suppose that the minimal-genus common stabilization of…

Zero-or-undefined index conjecture. Any pseudo vector field must have either index equal to zero or an undefined index.

Let $H$ be a surface other than $T^2$ or $S^2$, and let $\Delta(H)$ be its disc complex: vertices are isotopy classes of embedded discs intersecting $H$ exactly in their essential…

Let $H$ be a surface with topological index $n$. A surface is geometrically minimal if it is minimal with respect to the geometric notion used in the paper. Geometric minimality co…