3 problems

Large four-genus conjecture. The collection $\{\#^n K\}$ consists of $h$-solvable knots and contains knots with arbitrarily large smooth four-genera $g_4$.

Arbitrarily large four-genus conjecture. There are algebraically slice GA-knots with arbitrary large topological four-genus.

Let $Y$ be a closed, oriented, connected $3$--manifold, let $K\subset Y$ be a null-homologous knot, and let $F$ be a taut Seifert surface for $K$. Set … Let…