AI 中文总结
该研究借助大规模计算搜索和扩展算法，研究纽结的光滑不可定向4-亏格，识别出\(S^3\)中交叉数至多14且在\(B^4\)中界定莫比乌斯带的素纽结，扩展了相关已知例子并提供新数据。
AI 中文摘要
本研究通过大规模计算搜索来研究纽结的光滑不可定向4-亏格。计算了纽结不变量障碍，并扩展了现有计算算法，以识别\(S^3\)中交叉数至多为14且在\(B^4\)中界定莫比乌斯带的素纽结。研究结果显著扩展了不可定向4-亏格等于1的纽结的已知例子，并为不可定向4-亏格的研究贡献了新数据。
英文摘要
This study examines the smooth non-orientable $4$-genus of knots using a large-scale computational search. Knot invariant obstructions were computed, and existing computational algorithms were extended to identify prime knots in $S^3$ of crossing number at most $14$ that bound Möbius bands in $B^4$. The findings significantly expand the known examples of knots of non-orientable $4$-genus equal to $1$ and contribute new data relevant to the study of the non-orientable $4$-genus.
Comments29 pages, 8 figures
