Equivalent non‐isotopic spheres in 4‐manifolds
Equivalent non‐isotopic spheres in 4‐manifolds
复制标题
4 流形中的等效非同位素球体
DOI：
10.1112/topo.12121
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发表时间：
2018
影响因子：
1.1
通讯作者：
Hannah R. Schwartz
中科院分区：
文献类型：
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作者：
Hannah R. Schwartz
我们构造了无穷多个光滑定向的4 -流形，其中包含若干对光滑嵌入的2 -球，这些球不是拓扑上的同位素，而是通过一个环境微分同构诱导同构上的恒等而等效的。这些例子表明Gabai最近的“广义四维灯泡定理”并不能推广到任意的4‐流形。相比之下，我们还发现平滑嵌入的2‐球体既等效又具有拓扑同位素，但不是平滑同位素。
We construct infinitely many smooth oriented 4‐manifolds containing pairs of homotopic, smoothly embedded 2‐spheres that are not topologically isotopic, but that are equivalent by an ambient diffeomorphism inducing the identity on homology. These examples show that Gabai's recent ‘generalized 4D lightbulb theorem' does not generalize to arbitrary 4‐manifolds. In contrast, we also show that there are smoothly embedded 2‐spheres that are both equivalent and topologically isotopic, but not smoothly isotopic.