Homotopy versus isotopy: Spheres with duals in 4-manifolds
Homotopy versus isotopy: Spheres with duals in 4-manifolds
复制标题
同伦与同位素：4 流形中具有对偶的球体
DOI：
10.1215/00127094-2021-0016
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发表时间：
2019
影响因子：
2.5
通讯作者：
P. Teichner
中科院分区：
文献类型：
--
作者：
Rob Schneiderman;P. Teichner
David Gabai最近证明了在基本群中没有2-挠率的情况下，一个光滑的4维“灯泡定理”。我们将他的结果推广到具有任意基本群的4-流形上，证明了Mike Freedman和Frank Quinn的一个不变量对具有公共几何对偶的嵌入2-球面的“同伦蕴含同伦”是完全阻碍的。该不变量取值于由基本群中的2阶元生成的Z/2Z-向量空间中，并应用于自微分同态的解结数和伪同胚类。我们的方法还给出了Gabai定理的另一种方法，利用惠特尼圆盘的各种策略和可定向曲面上沿对偶圆的手术之间的基本同构。
David Gabai recently proved a smooth 4-dimensional "Light Bulb Theorem" in the absence of 2-torsion in the fundamental group. We extend his result to 4-manifolds with arbitrary fundamental group by showing that an invariant of Mike Freedman and Frank Quinn gives the complete obstruction to "homotopy implies isotopy" for embedded 2-spheres which have a common geometric dual. The invariant takes values in an Z/2Z-vector space generated by elements of order 2 in the fundamental group and has applications to unknotting numbers and pseudo-isotopy classes of self-diffeomorphisms. Our methods also give an alternative approach to Gabai's theorem using various maneuvers with Whitney disks and a fundamental isotopy between surgeries along dual circles in an orientable surface.
影响因子：
0.9
作者：
Gabai, David
通讯作者：
Gabai, David
单次稳定后 4 流形中表面的同位素
影响因子：
1.7
作者：
Auckly, Dave;Kim, Hee Jung;Melvin, Paul;Ruberman, Daniel;Schwartz, Hannah
通讯作者：
Schwartz, Hannah