AI 中文总结
研究透镜空间\(L(n,1)\)上紧接触结构的束缚数，借助\(d_3\)不变量、平面单值化分解限制及Durst - Kegel算法得出支持这些结构的平面开卷束缚分量数下界，算出\(L(n,1)\)上普遍紧接触结构束缚数为\(n\)。
AI 中文摘要
我们研究透镜空间\(L(n,1)\)上紧接触结构的束缚数。利用\(d_3\)不变量，结合平面单值化分解的限制以及从开卷计算\(d_3\)的Durst - Kegel算法，得到了支持这些接触结构的平面开卷的束缚分量数的下界。结果，我们计算出\(L(n,1)\)上普遍紧接触结构的束缚数，表明其等于\(n\)。
英文摘要
We study binding numbers of tight contact structures on the lens spaces $L(n,1)$. Using the $d_3-$invariant, together with restrictions on planar monodromy factorizations and the Durst-Kegel algorithm for computing $d_3$ from open books, we obtain lower bounds for the number of binding components of planar open books supporting these contact structures. As a consequence, we compute the binding number of the universally tight contact structures on $L(n,1)$, showing that it is equal to $n$.
Comments19 pages, 10 figures
