Comparing $h$-genera, Bridge-1 genera and Heegaard genera of knots

Ruifeng Qiu, Chao Wang, Yanqing Zou

Let $h(K)$, $g_H(K)$, $g_1(K)$, $t(K)$ be the $h$-genus, Heegaard genus, bridge-1 genus, tunnel number of a knot $K$ in the $3$-sphere $S^3$, respectively. It is known that $g_H(K)…