5 problems

Given a knot $K$, let the smooth non-orientable four-genus be … with $\gamma_4(K)=0$ when $K$ is slice. For a torus knot $T_{p,q}$, let $\vartheta(T_{p,q})$ denote the number of pi…

Higher-dimensional algebraic four-genus conjecture. In higher dimensions, this inequality should be an equality:

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…

Let $j$, $k$, and $l$ be integers satisfying … Here $g_4(K)$ denotes the four-genus of a knot $K$, $g_c(K)$ its concordance genus, and $g_3(K)$ its three-genus. Existence conjectur…