发表机构
The University of Texas at Austin; University of Southampton（德克萨斯大学奥斯汀分校; 南安普顿大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文建立单连通4维流形中局部平坦扭结曲面等价的充要条件，推广Lee-Wilczynski结果，证明射影平面等的相关结论，确定拓扑可延拓映射类群。
AI 中文摘要
本文建立了单连通4维流形中局部平坦的扭结曲面等价的充要条件。对于扭结群为ℤ_d的曲面，我们将Lee-Wilczynski的结果从球面推广到任意亏格的曲面，这些曲面允许是非定向的且带有边界。我们证明，大多数扭结群为ℤ₂且具有相同欧拉数的射影平面，由其外部的等变相交形式决定。我们还证明，素幂行列式的扭结在D⁴中以扭结群ℤ₂和给定欧拉数为界，最多可界定一条莫比乌斯带。消去结果为同调圆盘相对于边界的等价性提供了新判据。最后，我们确定了具有阿贝尔扭结群的扭结曲面的拓扑可延拓映射类群。
英文摘要
This paper establishes necessary and sufficient conditions for locally flat knotted surfaces in simply-connected $4$-manifolds to be equivalent. For surfaces with knot group $\mathbb{Z}_d$, we extend results of Lee-Wilczynski from spheres to surfaces of arbitrary genus; the surfaces are permitted to be nonorientable and have boundary. We prove that most projective planes with knot group $\mathbb{Z}_2$ and the same Euler number are determined by the equivariant intersection form of their exterior. We also prove that knots with prime power determinants bound at most one Moebius band in $D^4$ with knot group $\mathbb{Z}_2$ and a given Euler number. Cancellation results lead to new criteria for homologous discs to be equivalent rel. boundary. Finally, we determine the topological extendable mapping class group of knotted surfaces with abelian knot group.
Comments62 pages
