发表机构
Francis Marion University; Smith College; Boston College; University of California, Davis（弗朗西斯马林大学; 史密斯学院; 波士顿学院; 加州大学戴维斯分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文引入组合与图示方法研究4维Weinstein区域中的辛曲面，关联其多种分解并构造分支覆盖，证明紧Weinstein区域容许带划分的双截面。
AI 中文摘要
我们引入组合与图示方法，用以表示4维Weinstein区域中真嵌入的辛曲面。研究表明，正上升曲面（包含Stein区域中的复曲线与Lefschetz纤维化的多截面）可置于相对于Islambouli–Starkston的带划分双截面结构的桥位置。我们通过算法关联这类曲面的多种分解，包括横向带柄未链接图示、拟正因子化、带划分的桥双截面、阴影图示（曲面上的曲线）及带点单值因子化。我们还开发了一种沿正上升曲面构造Weinstein区域分支覆盖的新方法，结合Loi–Piergallini的工作，可得到Islambouli–Starkston的结论：每个紧Weinstein区域都容许带划分的双截面。
英文摘要
We introduce combinatorial and diagrammatic methods for representing properly embedded symplectic surfaces in 4-dimensional Weinstein domains. We show that positive ascending surfaces, which include complex curves in Stein domains and multisections of Lefschetz fibrations, can be placed in bridge position with respect to Islambouli--Starkston's bisection-with-divides structure on the Weinstein domain. We algorithmically relate various decompositions of such surfaces, including transverse banded unlink diagrams, quasipositive factorizations, bridge bisections with divides, shadow diagrams (curves on surfaces), and pointed monodromy factorizations. We also develop a new way to present branched covers of Weinstein domains along positive ascending surfaces, which, combined with work of Loi--Piergallini, recovers Islambouli--Starkston's result that every compact Weinstein domain admits a bisection with divides.
Comments31 pages, 21 figures, comments welcome!
