Geometric Analysis Seminar —— Comparing h-genera, Bridge-1 genera and Heegaard genera of knots
报告人：邹燕清（华东师范大学）
时间：2026-04-22 15:10-17:00
地点：智华楼四元厅（225）
【摘要】
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 $g_H(K)-1=t(K)\leq g_1(K)\leq h(K)\leq g_H(K)$. A natural question arises: when do these invariants become equal?
We provide the necessary and sufficient conditions for equality and use these to show that for each integer $n\geq 1$, there are infinitely many knots in each of the following three families:
\begin{center}
$A_{n}=\{K\mid h(K)=n<g_H(K)\}$. \\
$B_{n}=\{K\mid g_1(K)=n<h(K)\}$, \\
$C_{n}=\{K\mid t(K)=n<g_1(K)\}$, \\
\end{center}
This result resolves a conjecture of Morimoto, confirming that each of these families is infinite. This is a joint work with Ruifeng Qiu and Chao Wang.
