AI 中文总结
该研究证实Kearney的猜想，即满足1≤a≤b≤c的任意整数三元组(a,b,c)都可作为纽结的光滑切片亏格、光滑配边亏格与Seifert亏格实现。
AI 中文摘要
我们证明，每个满足1≤a≤b≤c的整数三元组(a,b,c)都可分别实现为纽结的光滑切片亏格、光滑配边亏格与Seifert亏格，这证实了Kearney的一个猜想。
英文摘要
We show that every triple of integers $(a,b,c)$ satisfying $1\leq a\leq b\leq c$ is realized as the smooth slice genus, smooth concordance genus, and Seifert genus of a knot, respectively. This proves a conjecture of Kearney.
Comments5 pages. Comments are welcome
